Answer:
8.04 seconds
Explanation:
Assuming that the child starts from rest at the bottom of the hill and travels until she comes to a stop, we can use the following kinematic equation:
v_f^2 = v_i^2 + 2ad
where v_f is the final velocity (which is zero since the child comes to a stop), v_i is the initial velocity (which is the velocity at the bottom of the hill), a is the acceleration (-0.392 m/s²), and d is the distance traveled.
We can solve for d:
d = (v_f^2 - v_i^2) / (2a)
= (0 - v_i^2) / (2-0.392)
= v_i^2 / 0.784
Since the child is sliding along flat snow-covered ground, there is no change in elevation, so we can use the distance traveled from the bottom of the hill to the stopping point as the distance d.
To find the time it takes for the child to travel this distance, we can use the following kinematic equation:
d = v_it + 0.5a*t^2
where t is the time and all other variables are as previously defined.
Substituting the expression for d obtained above, we get:
v_i^2 / 0.784 = v_it + 0.5(-0.392)*t^2
Solving for t, we get:
t = (2 * v_i) / 0.392
We still need to find the value of v_i, the initial velocity of the child at the bottom of the hill. To do so, we can use conservation of energy. The child starts at rest at the top of the hill, so all the initial energy is potential energy. At the bottom of the hill, all the potential energy has been converted to kinetic energy. Assuming no energy is lost to friction, we can equate these two energies:
mgh = 0.5mv_i^2
where m is the mass of the child, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the hill.
Solving for v_i, we get:
v_i = √(2gh)
Substituting this expression for v_i into the expression for t obtained earlier, we get:
t = (2 * √(2gh)) / 0.392
Plugging in the values of g, h, and a, we get:
t = (2 * √(29.820)) / 0.392 = 8.04 seconds
a 25.0-kg dog is trapped on a rock in the middle of a narrow river. a 66.0-kg rescuer has assembled a swing with negligible mass that she will use to swing down and catch the trapped dog at the bottom of her swing, and then continue swinging to the other side of the river. the ledge that the rescuer swings from is 5.0 m above the rock, which is not high enough so the rescuer and dog together can reach the other side of the river, which is 3.0 m above the rock. however, the rescuer can use a ladder to increase the height from which she swings. what is the minimum height of the ladder the rescuer must use so both dog and rescuer make it to the other side of the river? assume that friction and air resistance are negligible. show your work in the space below.
The minimum height of the ladder needed by the rescuer for a successful rescue of the dog is 5.944 meters
How to determine minimum height?To determine the minimum height of the ladder required for the rescuer and the dog to reach the other side of the river, use the conservation of energy principle. At the highest point of the swing, all of the gravitational potential energy of the system is converted into kinetic energy. At the lowest point of the swing, all of the kinetic energy is converted back into gravitational potential energy.
Let h be the height of the ladder above the rock where the swing is attached. Let v be the speed of the rescuer and the dog at the bottom of the swing, and let g be the acceleration due to gravity. Then, the conservation of energy equation is:
m_rgh + m_dgh = (m_r + m_d)gh' + (m_r + m_d)v²/2
where m_r and m_d are the masses of the rescuer and the dog, respectively, and h' is the height of the other side of the river.
We can solve for h' by rearranging the equation:
h' = [(m_r + m_d)gh + (m_r + m_d)v²/2 - m_rgh - m_dgh]/(m_r + m_d)
Substituting the given values:
h' = [(66.0 kg + 25.0 kg) × 9.81 m/s² × 5.0 m + (66.0 kg + 25.0 kg) × v²/2 - 66.0 kg × 9.81 m/s² × 5.0 m - 25.0 kg × 9.81 m/s² × 5.0 m]/(66.0 kg + 25.0 kg)
Simplifying the equation:
h' = (305.145 + 91.8725 - 323.46 - 122.625)/91 = 0.944 m
Therefore, the minimum height of the ladder that the rescuer must use is:
h - 5.0 m = 0.944 m
h = 5.944 m
So, the rescuer must use a ladder that is at least 5.944 meters high to swing over to the other side of the river with the dog.
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A conductor is in the shape of a small diameter cylindrical wire on the left and a large diameter cylindrical wire on the right as shown. An emf is applied between points A and B of the wire with a battery.
a. Which side has the larger current magnitude and why?
b. Which side has the larger potential difference magnitude, and why?
c. Which side has the larger drift velocity magnitude, and why?
d. Answers may include both sides are the same.
In case, when two cylindrical wires of different diameters are connected in series, an emf (electromotive force) is applied across the ends.
a. The side with the smaller diameter cylindrical wire on the left will have a larger current magnitude. This is because the current density, which is defined as the current per unit cross-sectional area of the wire, is inversely proportional to the cross-sectional area of the wire. Since the left side has a smaller cross-sectional area, it will have a larger current density and therefore a larger current magnitude.
b. The potential difference magnitude is the same on both sides. This is because the potential difference between two points is determined by the emf of the battery and is independent of the wire's properties. Therefore, the potential difference between points A and B is the same on both sides of the wire.
c. The side with the smaller diameter cylindrical wire on the left will have a larger drift velocity magnitude. This is because the drift velocity of electrons in a wire is proportional to the current density, which as stated above, is inversely proportional to the cross-sectional area of the wire. Since the left side has a smaller cross-sectional area, it will have a larger current density and therefore a larger drift velocity magnitude.
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A dragster is travelling east when the parachute opens and slows the dragster for 4.5 seconds at a rate of 10 m/s2 west. What was the dragster's change in velocity due to the parachute?
The dragster's change in velocity due to the parachute can be calculated using the kinematic equation:
Δv = aΔt
where Δv is the change in velocity, a is the acceleration, and Δt is the time interval during which the acceleration occurs. In this case, the dragster is initially travelling east, so its velocity is positive, and the parachute applies a force in the opposite direction, resulting in a negative acceleration.
Given that the acceleration is -10 m/s² (westward) and the time interval is 4.5 seconds, we can calculate the change in velocity as:
Δv = (-10 m/s²) x (4.5 s) = -45 m/s
Therefore, the dragster's change in velocity due to the parachute is -45 m/s (westward). This means that the dragster's velocity is reduced by 45 m/s in the westward direction over the 4.5-second interval during which the parachute is deployed.
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The change in velocity due to the parachute is -45 m/s east
What is velocity ?
Velocity is a vector quantity that describes the speed and direction of motion of an object. In other words, velocity is the rate at which an object changes its position in a specific direction.
Velocity is expressed in units of distance per time, such as meters per second (m/s) or kilometers per hour (km/h)
Velocity is different from speed, which is also a measure of the rate of motion but only describes how fast an object is moving, without taking into account the direction of motion.
we will use the formula :-
change in velocity = acceleration x time
where acceleration is the rate at which the dragster slows down, and time is the duration for which it slows down.
Here, the dragster is travelling east, and the parachute applies a force in the opposite direction (west), causing it to slow down. So, the acceleration is -10 m/s^2 (negative because it's in the opposite direction to the velocity).
The time for which the dragster slows down is 4.5 seconds.
Therefore, the change in velocity due to the parachute is:
change in velocity = acceleration x time
change in velocity = (-10 m/s^2) x (4.5 s)
change in velocity = -45 m/s east
Note that the velocity is negative because the dragster is slowing down, and it's still travelling east (i.e., in the positive direction).
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wo 0.20-kg balls, moving at 4 m/s east, strike a wall. Ball A bounces backwards at the same speed. Ball B stops. Which statement correctly describes the change in momentum of the two balls? a. Delta PB = Delta PA b. |Delta PB| = |Delta PA| c. |Delta PB| > |Delta PA| d. |Delta PB| < |Delta PA|e. Delta PB > Delta PA
The change in momentum of ball B is greater than the change in momentum of ball A (|Delta P_{B}| < |Delta P_{A}|) when two 0.20-kg balls, moving at 4 m/s east, strike a wall. Ball A bounces backwards at the same speed, while ball B stops.
When the two balls strike the wall, they experience a change in momentum due to the impulse of the wall.
The initial momentum of the system (two balls and the wall) is:
P_{initial}= m_{A}v_{A} + m_{B}v_{B}
After the collision, ball A bounces backwards with the same speed, so its final momentum is:
P_{A} = -m_{A}*v_{A}
Ball B stops, so its final momentum is:
P_{B} = 0
The total final momentum of the system is:
P_{final} = P_{A} + P_{B} = -m_{A}*v_{A}
The change in momentum of ball A is:
Delta P_{A} = P_{A} - m_{A}v_{A} = -2m_{A}*v_{A}
The change in momentum of ball B is:
Delta P_{B} = P_{B} - m_{B}v_{B} = -m_{B}v_{B}
Therefore, |Delta P_{B}| < |Delta P_{A}|, which means that option (d) is the correct answer.
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A car moves with this distance vs time function: 5 = 2t^2 + 2. what is the acceleration rate of the car? (clue: use derivatives) answer with number only, e.g. if it's 6t m/s^2, just write 6t
Answer:
just write 6t and the same
One object is placed on each shelf in the image above (W, X, Y, Z). The four objects have the same mass, 2.0 kg. Match each object to its potential energy.
Object W 7.84 J 15.7 J 13.4 J 0 J 23.5 J 5.62
Object X
Object Y
Object Z
Potential Energy of Object W, X, Y and Z are 0 J, 7.84 J, 15.7J and 23.5J, for better understand we have to know the meaning of potential energy.
What is Potential Energy?Potential energy in physics is the energy that an item retains as a result of its location in relation to other objects, internal tensions, electric charge, or other elements. Potential energy develops in systems having components whose configurations, or relative positions, determine the amount of the forces they apply to one another.
Potential Energy of an Object = m * g * h
Where, m = mass,
g = gravity, and
h = height
Potential Energy of Object W = 2 * 9.8 * 0
= 0 J
Potential Energy of Object X = 2 * 9.8 * 0.4
= 7.84 J
Potential Energy of Object Y = 2 * 9.8 * 0.8
= 15.68 J
≈ 15.7 J
Potential Energy of Object Z = 2 * 9.8 * 1.2
= 23.5 J
Therefore, Potential Energy of Object W, X, Y and Z are 0 J, 7.84 J, 15.7 J and 23.5 J.
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Two negative electrical charges are constrained so that they are very close together just after the charges are released their electrical potential energy will , their kinetic energy will and they will travel each other
Their electrical potential energy will decrease, their kinetic energy will increase, and they will travel towards each other.
Electrical potential energy of chargesWhen two negative charges are released and constrained to remain close together, the charges will be repelled by each other due to their opposite electrical charges.
This repelling force causes the charges to move away from each other, increasing their kinetic energy and decreasing their electrical potential energy.
Since they are constrained to remain close together, they will travel towards each other until they come into contact. At that point, the electrical potential energy will reach its minimum, and the kinetic energy will reach its maximum.
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Ignacio shares 2.1 liters of water equally into 7 containers. How many milliliters are in each container?(A) 0.3 milliliters(B) 300 milliliters(C) 2,100 milliliters(D) 14,700 milliliters
When Ignacio shares 2.1 liters of water equally into 7 containers, the milliliters in each container are 300 milliliters. Therefore, the correct option is B.
It is given that Ignacio shares 2.1 liters of water equally into 7 containers. To convert liters into milliliters, we multiply the given value by 1000. According to conversion unit, 1 liter = 1000 milliliters.
Therefore, 2.1 liters = 2.1 * 1000 = 2100 milliliters.
Now, to find milliliters in each container, we divide the total volume of water by the total number of containers. Therefore, the number of milliliters in each container is:2100 / 7 = 300 milliliters.
Hence, the correct answer is option (B) 300 milliliters.
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what complication is introduced in the excerpt? marco is unable to locate his friends in the busy park. the slide’s very long, uniformly charged cylinder have radius R and linear charge density λ.
a. Find the cylinder's electric field strength outside the cylinder, r≥R. Give your answer as a multiple of λϵ0.
Express your answer in terms of some or all of the variables R,r, and the constant II
b. Find the cylinder's electric field strength inside the cylinder, r≤R. Give your answer as a multiple of λϵ0.
Express your answer in terms of some or all of the variables R,r and the constant II
a. To find the electric field strength outside the cylinder, E = λ/(2πϵ0r), where r≥R. b. To find the electric field strength inside the cylinder, E = λr/(2πϵ0R^2), where r≤R.
the electric field strength inside and outside a charged cylinder can be determined using the formulas E = λr/2πϵ0R^2 and E = λ/2πϵ0r, respectively. The electric field strength outside the cylinder is proportional to the linear charge density and inversely proportional to the distance from the center of the cylinder. On the other hand, the electric field strength inside the cylinder is proportional to both the linear charge density and the distance from the center of the cylinder, the slide’s very long, uniformly charged cylinder have radius R and linear charge density λ. a. Find the cylinder's electric field strength outside the cylinder, r≥R. but inversely proportional to the square of the radius of the cylinder. These formulas can be used to solve problems involving charged cylinders and their electric fields.
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A current is set up in a wire loop consisting of a semicircle of radius 4.00 cm, a smaller concentric semicircle, and two radial straight lengths, all in the same plane. Figure shows the arrangement but is not drawn to scale. The magnitude of the magnetic field produced at the center of curvature is 47.25μT.The smaller semicircle is then flipped over (rotated) until the loop is again entirely in the same plane. The magnetic field produced at the (same) center of curvature now has magnitude 15.75μT, and its direction is reversed from the initial magnetic field. What is the radius of the smaller semicircle?
The radius of the smaller semicircle is 2cm.
[tex]B_1= \frac{u0I}{T} (\frac{1}{R_1} -\frac{1}{R_2} )[/tex]
[tex]B_2= 2.\frac{u0I}{2} \frac{1}{R_2} =\frac{uoI}{R_2}[/tex]
We can now solve for r by setting $B_1=-B_2
[tex]\frac{u0I}{2} (\frac{1}{4} -\frac{1}{r} )= \frac{uoI}{r}[/tex]
r= 2cm
A magnetic field is a force field that is created by moving electric charges. It is a fundamental concept in electromagnetism, and it is essential for many technologies, such as motors, generators, and MRI machines.
A magnetic field is typically represented by lines of magnetic flux that show the direction of the force. These lines of flux are generated by electric currents, whether they are moving charges or stationary ones. The strength of a magnetic field is measured in units of teslas or gauss, depending on the system of measurement used.
Magnetic fields have both magnitude and direction and can interact with other magnetic fields or with magnetic materials, such as iron or steel. The interaction between magnetic fields and moving charges can cause the charges to change direction, which is the basis for motors and generators.
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what is large solar eruptions that occur near sunspots
Large solar eruptions near sunspots are known as coronal mass ejections (CMEs).
what are CMEs?Coronal mass ejections (CMEs) are huge explosions of plasma and magnetic fields from the sun's corona, the outermost layer of the sun's atmosphere. Sunspots are areas on the sun's surface where the magnetic field is much stronger than surrounding regions, which can lead to the buildup of energy that can trigger a CME.
CMEs can release vast amounts of energy and can cause solar flares, geomagnetic storms, and other space weather phenomena that can affect our planet.
They can also pose a danger to astronauts and satellites in space. Scientists study CMEs to better understand the sun's behavior and how it affects Earth and the rest of the solar system.
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A pendulum comprised of a metal ball attached to a light string of length L undergoes simple harmonic motion with a period given by
T = 2 π sqrt(L/g). If the ball is made positively charged and the pendulum is swung in an electric directed towards the center of the earth. Which statement is true?
Not enough information
The period is unchanged
The period decreases
The period increases
Not enough information is given to determine whether the period would decrease, increase, or remain unchanged.
The period indicates the time required for a complete oscillation, the frequency indicates the number of oscillations that occur in one second, and the angular frequency indicates the magnitude of the rotational speed.
The period of a pendulum comprised of a metal ball attached to a light string of length L undergoing simple harmonic motion is given by T = 2 π sqrt(L/g). If the ball is made positively charged and the pendulum is swung in an electric directed towards the center of the earth, then not enough information is given to determine whether the period would decrease, increase, or remain unchanged.
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A slingshot sends a stone vertically upward from a height of 20 feet above a pool of
water. The starting speed of the stone is 90 feet per second. Its distance in feet, d.
above the water is given by the equation:
d-20+90t-16t^2, where t is the time in seconds after the launch.
Drag statements to the table to show what each coordinate labeled on the graph
represents in this problem situation.
the height of the stone when it is launched
the time when the stone hits the water
the time when the stone is launched the maximum height of the stone
the time when the stone reaches its maximum height
Coordinate
A
the height of the stone when it hits the water
What the Coordinate Represents
DRAG AND DROP
AN ITEM HERE
DRAG AND DROP
AN ITEM HERE
DRAG AND DROP
DRAG AND DROP
Coordinate , A - the height of the stone when it hits the water. A slingshot sends a stone vertically upward from a height of 20 feet above a pool of water.
What the Coordinate Represents?The coordinate A represents the height of the stone when it hits the water. When the stone hits the water, its height above the water surface is zero.
So, we can set the expression for the stone's height equal to zero and solve for t to find the time when the stone hits the water. The height of the stone when it is launched is given as 20 feet, which is a fixed value in this problem.
The time when the stone is launched is also a fixed value, which is zero. The maximum height of the stone is the highest point the stone reaches above its initial height of 20 feet. The time when the stone reaches its maximum height is the time at which the vertical velocity of the stone becomes zero.
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A shell is shot with an initial velocity, v0 of 20m/s,at an angle of θ0= 60 with the horizontal. At thetop of the trajectory, the shell explodes into two fragments ofequal mass. One fragment, whose speed immediately after theexolosion is zero, falls vertically. How far from the gun does theother fragment land, assuming that the terrain is level and thatair drag is negligible?
When the shell is shot with an initial velocity 20m/s with angle 60 the distance d the other fragment lands from the gun is 69.3 m.
The other fragment will land a distance d away from the gun, where d is determined by the initial velocity, v₀ of 20 m/s and the angle, θ₀ of 60°, from which the shell was launched. The trajectory of the fragment is affected by the shell's velocity, its gravitational potential energy, and its kinetic energy. When the shell explodes, it releases all of its kinetic energy, which is shared among the two fragments. The other fragment will travel a distance d which is determined by the total energy, E and its initial velocity, v0.
To calculate d, we can use the equation:
d = (2E/m)1/2sin(2θ₀) / v₀,
where m is the mass of the fragment and E is the total energy.
Therefore, the distance d the other fragment lands from the gun is given by: d = (2E/m)1/2sin(2θ₀) / v₀
= (2×202×sin(120°))/20
= 40×sin(120°) = 40×√3 = 69.3 m.
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A 1500 kg car is moving to the right with a speed of 20.0 m/s when it collides with a wall and reboubds at a speed of 5.00 m/s.
If the collision lasts for 250 ms, then the magnitude of the average force acring on the car is _____ kN (the answer is 150 but I'm not sure how)
pls help!!
Answer:
See below.
Explanation:
When the 1500 kg car collides with the wall and rebounds at a speed of 5.00 m/s, we can calculate the change in the car's velocity using the following formula:
Δv = v2 - v1
Where Δv is the change in velocity, v2 is the final velocity, and v1 is the initial velocity. Substituting the given values, we get:
Δv = 5.00 m/s - 20.0 m/s
Δv = -15.0 m/s
The negative sign indicates that the direction of the car's velocity has reversed, or that the car is now moving to the left. To calculate the magnitude of the change in velocity, we take the absolute value:
|Δv| = |-15.0 m/s|
|Δv| = 15.0 m/s
Therefore, the magnitude of the change in velocity is 15.0 m/s.
Now,
To find the magnitude of the average force acting on the car during the collision, we can use the impulse-momentum theorem, which states that:
Impulse = change in momentum
Average force = Impulse / time
The change in momentum of the car is given by:
Δp = mΔv
where Δv is the change in velocity calculated in the previous answer and m is the mass of the car.
Δp = 1500 kg × (-15.0 m/s)
Δp = -22500 kg·m/s
The impulse acting on the car during the collision is equal to the change in momentum:
Impulse = Δp = -22500 kg·m/s
To find the magnitude of the average force acting on the car during the 250 ms collision, we divide the impulse by the duration of the collision:
Average force = Impulse / time
Average force = -22500 kg·m/s / 0.250 s
Average force ≈ -90,000 N
The negative sign indicates that the force is in the opposite direction of the car's motion, or to the left. Therefore, the magnitude of the average force acting on the car during the collision is approximately 90,000 N.
Predict how the horizontal component of the velocity will change with time after the projectile is fired.
A) It stays constant. B) It continuously decreases. C) It continuously increases. D) It first increases and then decreases. E) It first decreases and then increases.
The correct option is option A) It stays constant.The horizontal component of the velocity will remain constant with time after the projectile is fired.
Projectile motion is the movement of an object that has been thrown, launched, or shot into the air. The object is called a projectile, and its path is referred to as its trajectory. Projectile motion can be predicted and analyzed by physics, but it is not as straightforward as it may seem. The following are some of the properties of projectile motion: Acceleration due to gravity (9.8 m/s²) Act of the horizontal and vertical components of velocity (v) Path of the projectile in a parabolic shape. The horizontal component of the velocity will remain constant with time after the projectile is fired.
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what is the main factor to consider when planning your vessel’s approach to a dock where you intend to tie up?
Wind direction and speed, together with current, tides, vessel maneuverability, and the appropriate angle and speed, are the key factors to take into account when approaching a dock for a tie-up.
The wind's direction and speed, together with the current, tides, and the vessel's maneuverability, are the key factors to take into account when preparing a vessel's approach to a dock where you wish to tie up. To guarantee a secure tie-up, it is essential to approach the dock at the right angle and speed while taking these considerations into mind. The size and design of the dock, its height above the water, and the availability of mooring lines and fenders are also additional crucial factors. A good tie-up can also be attributed to effective communication and cooperation between the crew and any other people on the dock.
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3. a vertical spring stretches 3.9 cm when a 10-g object is hung from it. the object is replaced with a block of mass 25 g that oscillates up and down in simple har- monic motion. calculate the period of motion.
The period of motion of a vertical spring that stretches 3.9 cm when a 10-g object is hung from it is 0.883 s.
Period of motion = 2π√(m/k) Where,m = mass of the object k = spring constant. Given data:Spring stretches = 3.9 cm. Mass of the object = 10 g = 0.01 kg. New mass = 25 g = 0.025 kg. Formula used:Period of motion = 2π√(m/k). Calculation:First we need to calculate the spring constant using the formula below:F = -kx Where,F = force (in N)x = extension (in m)k = spring constant.We have the value of x, and we can calculate the force.F = ma Where,a = acceleration (in m/s²)m = mass (in kg)
We can assume that acceleration is the same as gravity (9.8 m/s²) since the object is hung vertically.F = (0.01 kg) × (9.8 m/s²) = 0.098 N.Since the spring stretches by 3.9 cm = 0.039 m, we can calculate the spring constant:k = F/x = 0.098 N / 0.039 m = 2.51 N/m.Now we can calculate the period of motion using the formula below:Period of motion = 2π√(m/k)Period of motion = 2π√(0.025 kg / 2.51 N/m).Period of motion = 0.883 s. Therefore, the period of motion is 0.883 s.
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the eoq model is most relevant for which one of the following?
inventory management, the eoq model is most relevant for inventory management. In order to reduce the overall cost of inventory, it helps to determine the ideal order quantity that a business should produce or buy.
In operations and inventory management, the EOQ (Economic Order Quantity) model is a widely used mathematical model. In order to reduce the overall cost of inventory, it helps to determine the ideal order quantity that a business should produce or buy. The most cost-effective order quantity is determined by the model, which takes into account a variety of inventory costs, including ordering, holding, and stock-out costs. The EOQ model enables businesses to maintain suitable inventory levels while reducing inventory costs. As a result, it is a crucial tool for any company that manages inventory, from manufacturing to retail.
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A ball is attached to the end of a string it swung at a vertical circle of three of 0.33M what is the minimum velocity that the ball must have to make it around the circle
Answer:
To make it around the circle, the tension in the string must provide the necessary centripetal force to keep the ball moving in a circle. At the top of the circle, the tension in the string must provide all the force to keep the ball moving in a circle. At the bottom of the circle, the tension in the string must provide the centripetal force in addition to the force of gravity.
We can use the centripetal force formula to solve for the minimum velocity: F_c = m * a_c
where F_c is the centripetal force, m is the mass of the ball, and a_c is the centripetal acceleration.
At the top of the circle, the centripetal force is equal to the tension in the string: F_c = T
where T is the tension in the string.
At the bottom of the circle, the centripetal force is equal to the sum of the tension in the string and the force of gravity:
F_c = T + mg
where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s^2), and T is the tension in the string.
The centripetal acceleration is given by: a_c = v^2 / r
where v is the velocity of the ball and r is the radius of the circle.
Since the circle has a radius of 0.33 m, we can substitute this into the equation for a_c: a_c = v^2 / 0.33
Combining these equations, we get:
At the top of the circle: T = m * v^2 / 0.33
At the bottom of the circle: T + mg = m * v^2 / 0.33
We can solve for the minimum velocity by using these two equations to eliminate the tension in the string: m * v^2 / 0.33 + mg = m * v^2 / 0.33
Simplifying this equation, we get: v = sqrt(0.33 * g)
Plugging in the values, we get: v = sqrt(0.33 * 9.8) = 1.81 m/s
Therefore, the minimum velocity that the ball must have to make it around the circle is 1.81 m/s
a bullet is shot horizontally from shoulder height (1.2 m) with an initial speed of 682 m/s. (a) how much time elapses (in s) before the bullet hits the ground? s (b) how far does the bullet travel horizontally (in m)? m
A bullet is shot horizontally from shoulder height (1.2 m) with an initial speed of 682 m/s.
The kinematic equation of motion for the horizontal motion of an object
i.e, s = vt
Where s is the displacement,
v is the initial speed,
and t is the time.
(a) Initial vertical velocity (u) = 0 m/s
Acceleration (a) g = 9.8 m/s²
(since the bullet is moving vertically downwards)
Vertical displacement (s)H = 1.2 m
By using the following kinematic equation of motion: v² = u² + 2as
Putting the values in the above equation,
0² = 682² + 2 (-9.8) (1.2)
s = 47.999m
since the bullet will hit the ground at 48 m.
Therefore, the time taken by the bullet to hit the ground is given by the
s = ut + 1/2 a t²
Hence, 48 = 0 × t + 1/2 (9.8) t²
t = 3.91 seconds.
(b) horizontal velocity (u) = 682 m/s
Time (t) = 3.91 seconds.
By using the following kinematic equation of motion:
s = ut
Putting the values in the above equation,
s = 682 × 3.91s
= 2668.62m
Thus, the bullet will travel a distance of 2668.62 m.
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In order to join more than two datasets with only visual recipes, which of the following solutions is correct and why? It is not possible to join more than two datasets at a time with the Join recipe. Perform multiple Join recipes instead. Although only two datasets can be added in the Join recipe creation dialog, more datasets can be added on the Join step. Provided it is a left join, a single Join processor of the Prepare recipe is capable of joining more than two datasets at a time. None of these.
The correct solution is "Perform multiple Join recipes instead." It is not possible to join more than two datasets at a time with the Join recipe. Each Join recipe can only join two datasets at a time. To join more than two datasets, multiple Join recipes should be used in sequence.
When joining more than two datasets with visual recipes, it is possible to perform multiple Join recipes instead of joining all of them together at once. This is because the Join recipe only allows for the addition of two datasets at a time during the creation dialog, but more datasets can be added on the Join step.For instance, if there are four datasets to be joined, the first two can be joined together using the Join recipe. Then, the resulting dataset can be joined with the third dataset, followed by joining the resulting dataset with the fourth dataset. This way, all four datasets can be joined together.There is a possibility of using a single Join processor of the Prepare recipe for joining more than two datasets at a time, but only if it is a left join. However, this method is not advisable as it may result in inaccuracies and inconsistencies.The Join recipe is a recipe that enables the merging of two datasets into a single dataset based on a shared column. This recipe is useful for cleaning and integrating data from different sources into a single dataset. The Join recipe allows for the selection of the type of join to perform, such as inner join, left join, right join, and full outer join.The Prepare recipe is a recipe that is used to transform and clean datasets in preparation for analysis. This recipe allows for the selection of processors that carry out various functions such as renaming columns, filtering rows, and calculating new columns.
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a rectangular field is twice as long as it is wide. the perimeter of the field is 450 yards. find the dimensions of the field. you must find an equation to represent the situation and solve.
The dimensions of the field can be found to be 75 yards in width and 150 yards in length.
Given:
Let the width of the rectangular field be x
Length of the rectangular field = 2x
Perimeter of the rectangular field = 450 yards
Formula Used:
Perimeter of a rectangle = 2 (l + w)
Where l and w are the length and width of the rectangle respectively.
Solution:
As per the question,
Perimeter of the rectangular field = 450 yards
Therefore, 2(Length + Width) = 450
2(x + 2x) = 450
2(3x) = 450
6x = 450
x = 75
Therefore, the width of the rectangular field is 75 yards
Length of the rectangular field = 2x = 2 × 75 = 150 yards
Hence, the dimensions of the field are 75 yards by 150 yards.
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you have an rc circuit with a time constant of 5.35 s. if the total resistance in the circuit is 231.2 k , what is the capacitance of the circuit (in f)? don't type the units into the answer box.
The capacitance of the circuit (in f) is 2.31×10⁻⁵F for the rc circuit with a time constant of 5.35 s. if the total resistance in the circuit is 231.2 k.
What is the capacitance of the circuit?The capacitance of an RC circuit can be calculated using the equation C = τ/(R), where τ is the time constant, R is the total resistance, and C is the capacitance. For this RC circuit, the time constant is 5.35s and the total resistance is 231.2 k. Therefore, the capacitance is 5.35s/(231.2k) = 2.31×10⁻⁵F.
Time constant of the RC circuit, τ = 5.35s
Total resistance in the circuit, R = 231.2 kΩ = 231200 Ω
Capacitance of the circuit = ?
We know that, Time constant (τ) of a RC circuit = R × C.
where, R is the resistance in ohms, C is the capacitance in farads. Substitute the given values in the above equation:
τ = RC
5.35 s = R × C231200 Ω × C = 5.35 s
C = 5.35 s / 231200 Ω
C = 2.31 × 10⁻⁸ F.
Therefore, the capacitance of the circuit is 2.31 × 10⁻⁸ F.
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5. (10 pts) The shedding frequency based on the analysis of Question 3 is to be determined through the use of a small-scale model to be tested in a water tunnel. For the specific bridge structure of interestD=20 cmandH=300 cm, and the wind speedVis25 m/s. Assume the air is at MSL ISA conditions. For the model, assume that D m=2 cm. (a) Determine the length of the model Hm needed for geometric scaling. (b) Determine the flow velocity Vm needed for Reynolds number scaling. (c) If the shedding frequency for the model is found to be 27 Hz, what is the corresponding frequency for the full-scale structural component of the bridge? Notes: Refer to the eBook for the properties of air. Assume the density of water rho H2O= 1000 kg/m3 and the dynamic viscosity of water μ H2O=1×10^−3 kg/m/s.
Length of the model Hm = 12 cm. The flow velocity Vm = 5 m/s. Frekuensi yang sesuai untuk skala penuh komponen struktural jembatan adalah 2,7 Hz.
To determine the length of the model, Hm, for geometric scaling, you must use the relationship Hm/H = Dm/D, where Dm is the model's diameter, D is the full scale structure's diameter, and Hm and H are the model and full-scale heights, respectively. Substituting in the given values, we have Hm/300 cm = 2 cm/20 cm, which can be solved for Hm to find that Hm = 12 cm.
To determine the flow velocity Vm for Reynolds number scaling, you must use the relationship Vm/V = sqrt(rhoH2O/rho)*(D/Dm), where rho is the air density and rhoH2O is the water density. Substituting in the given values, we have Vm/25 m/s = sqrt(1000 kg/m3/1.225 kg/m3)*(20 cm/2 cm). Solving for Vm, we find that Vm = 5 m/s.
To determine the shedding frequency for the full-scale structure of the bridge, we must use the relationship f/fmodel = (Vmodel/V)*(Dmodel/D). Substituting in the given values, we have f/27 Hz = (5 m/s/25 m/s)*(2 cm/20 cm). Solving for f, we find that the corresponding frequency for the full-scale structural component of the bridge is 2.7 Hz.
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A small mass rests on a horizontal platform which vibrates vertically in simple harmonicmotion with period 0.50 s.(a) Find the maximum amplitude of the motion which will allow the mass to stay in contactwith the platform throughout the motion.The maximum acceleration that will allow the object to remain in contact with theplatform at all times is when amax = g = 9:81 m/s.But amax = !222A = (2¼=T )A ) 9:81 = (2¼=0:5)2A = 158A ) A = 0:062 m
The maximum amplitude of the motion which will allow the mass to stay in contact with the platform is 0.062 m.
This can be calculated by using the equation amax = (2π/T)2A, where A is the maximum amplitude, and T is the period of the motion. In this case, T is 0.50 s, and g (the acceleration due to gravity) is 9.81 m/s2, so we can calculate A:
A = (2π/T)2g = (2π/0.50)2 × 9.81 = 158 × 9.81 = 1543.38
Therefore, A = 1543.38/158 = 9.81 m/s2 = 0.062 m.
Alternatively: given,T = 0.50 s,The acceleration due to gravity, g = 9.81 m/s²Maximum acceleration, amax = g = 9.81 m/s². The maximum acceleration that will allow the object to remain in contact with the platform at all times is when amax = !222A = (2π/T )A ) 9.81 ...(1)From the equation (1), we get 158 A = 9.81 (2π/0.50)A = (9.81 (2π/0.50))/158 = 0.062 m. Therefore, the maximum amplitude of the motion which will allow the mass to stay in contact with the platform throughout the motion is 0.062 m.
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Three engines operate between reservoirs separated in temperature by 300 K. The reservoir temperatures are as follows:Engine A: Th = 1000 K, Tc = 700 K;Engine B: Th = 800 K, Tc = 500 K;Engine C: Th = 600 K, Tc = 300 K.Rank the engines in order of theoretically possible efficiency, from highest to lowest.
The order of theoretically possible efficiency, from highest to lowest is Engine C, Engine B, and Engine A.
The theoretical efficiency of a Carnot engine is given by the formula:
Efficiency = 1 - T_{c} / Th
where Th and T_{c} are the temperatures of the hot and cold reservoirs, respectively.
Using this formula, we can calculate the efficiency of each engine.
For engine A, we have:
Efficiency = 1 - T_{c} / Th = 1 - 700 K / 1000 K = 0.3 or 30%
For engine B, we have:
Efficiency = 1 - T_{c} / Th = 1 - 500 K / 800 K = 0.375 or 37.5%
For engine C, we have:
Efficiency = 1 - T_{c} / Th = 1 - 300 K / 600 K = 0.5 or 50%
Therefore, the ranking of engines from highest to lowest theoretical efficiency is: Engine C (50%) > Engine B (37.5%) > Engine A (30%)
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An 8 kg ball travelling at 4 m/s collides head on with a 3 kg ball travelling at 14 m/s. The balls bounce off each other and travel back the way they came. The 8 kg ball travels away at 2 m/s. calcukate: the velocity of the 3 kg ball after the collision.
The velocity of the 3 kg ball after collision with the 8 kg ball is 2 m/s.
What is velocity?Velocity is the rate of change of displacement.
To calculate the velocity of the of the 3 kg ball after collision, we use the formula below.
Formula:
MU+mu = MV+mv................... Equation 1Where:
M = Mass of the bigger ballm = Mass of the smaller ballU = Initial velocity of the bigger ballu = Initial velocity of the smaller ballV = Final velocity of the bigger ballv = Final velocity of the smaller ballFrom the question,
Assuming: The bigger ball is initial traveling to the right and lets take right to be positive.
Given:
M = 8 kgm = 3 kgU = 4 m/su = -14 m/sV = - 3 m/sSubstitute these values into equation 1 and solve for v
(8×4)+(-14×3) = (-2×8)+(3×v)32-42 = -16+3v3v = -10+163v = 6v = 6/3v = 2 m/sHence, the velocity of the 3 kg ball is 2 m/s.
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what are some factors that may have caused errors in your measured values, and how could these have been avoided? how do the measured values for impulse compare to the calculated values for change in momentum?
Some factors which may cause errors in the measured values include inaccurate measuring instruments, poor technique, incorrect calculations, and poor experimental conditions.
What factors cause error in measured values?Some factors that may have caused errors in your measured values are: inaccurate measuring instruments, poor technique, incorrect calculations, and poor experimental conditions.
The impulse is equal to the change in momentum. The measured values for impulse and calculated values for change in momentum should be equal. The impulse is equal to the product of the average force applied to the object and the time during which it was applied. The change in momentum is equal to the product of the object's mass and its change in velocity, and it can be calculated using the equation Δp = mΔv.
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(Astronomy)
If humans one day encountered aliens, what measurement system would we most likely share with them?
light speed
parsecs
astronomical unit
miles
ANSWER: A (Light speed.)
Answer:
If humans one day encountered aliens, it is unlikely that we would share any existing measurement system with them. Different civilizations could have different systems of measurement and it would be necessary to establish a common framework to facilitate communication and understanding. However, scientists have proposed the use of mathematical constants and physical properties of the universe as a basis for a universal system of measurement that could be shared by any intelligent species, such as the speed of light, the Planck length, and the gravitational constant.