The area of the surface generated is approximately 1180.89 square units.
To find the area of the surface generated when the curve y = 8√x is revolved about the x-axis, we can use the formula:
[tex]A = 2\pi \int_a^b y ds[/tex]
where a and b are the limits of integration, y is the function to be revolved, and ds is an element of arc length.
To find ds, we can use the formula:
[tex]ds = \sqrt{1 + {(\dfrac{dy}{dx}})^2} dx[/tex]
where dy/dx is the derivative of y with respect to x.
In this case, we have y = 8√x,
So dy/dx = 4/√x.
Therefore, [tex]ds = \sqrt{1 + \dfrac{4}{\sqrt{x}}^2} dx[/tex]
[tex]= \dfrac{4}{\sqrt x} \times \sqrt{x+4}\ dx[/tex]
Substituting this into the formula for the surface area, we get:
[tex]A = 2\pi \int_9^{20} y \times 4/√x \times \sqrt{x+4} dx\\= 8\pi \int_9^{20} \sqrt x \times \sqrt{x+4}\ dx\\= 8\pi \int_9^{20} (x+4) dx\\= 8\pi [\dfrac{1}{2}\times (20^2+420) - \dfrac{1}{2}\times (9^2+49)][/tex]
= 1180.89
Therefore, the area of the surface generated is approximately 1180.89 square units.
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How do you calculate buoyant force?
The Buoyant force operates on an item when it is immersed in a fluid (liquid or gas), and it is equal to the weight of the fluid displaced by the object. You may use the following formula to determine buoyant force:
Buoyant force equals the weight of the fluid displaced by the item.
The object's displacement of fluid equals the density of the fluid times the volume of fluid displaced. As a result, the formula for determining buoyant force is as follows:
Buoyant force = fluid density x volume displaced x gravity
where gravity is the gravitational acceleration.
To use this method, you must first determine the density of the fluid as well as the volume of fluid displaced by the item. The volume of fluid displaced equals the volume of the submerged item in the fluid. If the entire item is submerged, the volume of fluid displaced equals the object's volume.
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What is the uncertainty of a cm ruler?
The ±0.05 cm means that your measurement may be off by as much as 0.05 cm above or below its true value. This value is called the uncertainty or the precision of the instrument.
In physics, uncertainty refers to the degree of doubt or error that is associated with a measurement or calculation. Uncertainty can arise from a variety of factors, such as limitations of measurement equipment, inherent randomness in physical systems, or the limitations of mathematical models.
Uncertainty is an important concept in physics because it is impossible to make perfectly precise measurements or predictions, and understanding the degree of uncertainty associated with a measurement is critical for evaluating the reliability of experimental results and theoretical models. By accounting for uncertainty, physicists can determine the level of confidence that can be placed in a measurement or calculation and make more accurate predictions and decisions.
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What kind of charge does each object have?
A. Both are negatively charged.
B. Both are positively charged.
C. A is positively charged, and B is negatively charged.
D. A is negatively charged, and B is positively charged.
Answer: The answer is D.
Explanation:
The way A is shooting arrows away means its a negative current. On the other hand B is taking them in making B positive. and that's why the answer is D.
an infinitely long insulating cylinder of radius r has a volume charge density that varies with the radius as given by the following expression where rho0, a, and b are positive constants and r is the distance from the axis of the cylinder.
The expression for the volume charge density of an infinitely long insulating cylinder of radius r is given by:
ρ(r) = ρ₀ / (1 + (r/a)^2)^(3/2) * (1 – (r/b)^2)^(3/2)
where ρ₀, a, and b are positive constants, and r is the distance from the axis of the cylinder. This expression shows that the charge density decreases with increasing radius, as the denominator increases more quickly than the numerator.
Additionally, the constants ρ₀, a, and b all affect the rate at which the charge decreases with increasing radius. The larger the value of ρ₀, the more quickly the charge density decreases with increasing radius, so it is important to choose the correct values for these constants in order to accurately model the charge distribution.
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Why the force experienced is reduced when a boxer is moving away from a punch
The time is increased and as a result the effect of force is decreased since force is inversely proportional to time, hence the force decreases.
Impact forces are inversely correlated with collision time and inversely correlated with the change in momentum that occurs during a collision.
The power felt by a boxer as they move away from a blow is lessened since the strike has more time to make contact with them. Impulse is the result of the power and the moment of application, and this notion explains why "rolling with the punches" in boxing is effective.
Rolling against a punch shortens the time but decreases the force of contact.
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What is conduction in energy transfer?
Conduction is the transfer of heat energy between two objects or substances that are in contact with each other, due to a temperature difference between them.
Conduction is the transfer of heat or electrical energy through a material or substance, without any visible movement of the substance itself. It occurs in solids, liquids, and gases, but is most efficient in solids, where the molecules are tightly packed and can easily transfer energy from one to the other. In conductive materials, heat or electrical energy is transferred by the flow of electrons, atoms, or molecules from a region of higher energy to a region of lower energy.
The rate of conduction depends on several factors, including the temperature difference between the two regions, the physical properties of the material, and the distance between the two regions. Conduction is an important process in everyday life, and understanding its principles is crucial in many fields, including engineering, physics, and materials science.
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In Wikipedia, look up "Kelvin" and answer this question: The Kelvin scale is a temperature scale like the Celsius temperature scale (1 deg C = 1 deg K), but they are shifted from each other. Kelvin is the predominantly used for scientific purposes. What is the lowest theoretical temperature that can exist in the universe on the Kelvin scale?
the lowest theoretical temperature that can exist in the universe on the Kelvin scale is zero kelvin (0 K)
Absolute zero, technically known as zero Kelvin, corresponds to -273.15 degrees Celsius or -459.67 degrees Fahrenheit and marks the point on the thermometer where the system reaches the lowest possible energy or thermal motion. However, there is a catch.
Absolute zero cannot be reached.
Two of the most commonly used temperature measurement scales in the thermometer industry are the Kelvin and Celsius scales. A value of 1 degree on the Kelvin scale is the same as a value of 1 degree on the Celsius scale. That is, the temperature difference or temperature change is the same on both scales.
You can use this relationship to convert Celsius to Kelvin.
Celsius = (Kelvin - 273.15)
0r
Kelvin = (Celsius + 273.15)
The Kelvin to Celsius formula is used to convert temperature expressed in Kelvin to Celsius.
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the best long-term solution to the pressing energy problems in the united states is:________
The best long-term solution to the pressing energy problems in the United States is a combination of different strategies that aim to increase the use of renewable energy sources, reduce energy consumption, and improve energy efficiency.
Some of these strategies are:
Transitioning to renewable energy sources: The United States needs to shift its reliance on fossil fuels to renewable energy sources such as wind, solar, hydro, and geothermal. This will not only help to reduce greenhouse gas emissions but also create jobs and stimulate economic growth.
Improving energy efficiency: Another important step is to improve energy efficiency in buildings, industries, and transportation. This can be achieved by using energy-efficient technologies, building design, and better transportation planning.
Investing in research and development: There is a need for more investment in research and development of new energy technologies that can help to address the pressing energy problems. This can include new battery technologies, advanced nuclear power, and carbon capture and storage.
Encouraging behavior change: Another crucial step is to encourage behavior change in individuals and businesses to reduce energy consumption. This can be achieved through education, awareness campaigns, and incentives for energy-efficient behavior.
Overall, the best long-term solution to the pressing energy problems in the United States will require a comprehensive approach that integrates these and other strategies to create a more sustainable and resilient energy system.
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A 0. 400-kg rock is swung in a circular path and in a vertical plane on a 0. 5-m length string. At the top of the path, the angular speed is 10. 0 rad/s. What is the tension in the string at that point?.
That location has a 16.72 N string tension.
The acceleration at the bottom of the circle is merely normal (because there are no forces acting in the horizontal direction) and equal to the centripetal acceleration as follows:
ac = v2/r = 2*r T- m*g = m*2*r
The following is how we can solve for T using the givens as replacements:
T = m* (2*r+g) = 0.4 kg*((8.00)2 rad/sec2*0.5m)+9.8 m/s2) = 16.72 N.
What does angular vs. linear speed mean?The pace at which something rotates is its angular speed, which is measured in terms like r.p.m, degrees per seconds, etc. The linear speed is how quickly a point on the edge of an object moves in a circle around the item's center.
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What does storm signal number 1 mean?
Storm signal number 1 is a form of weather caution issued via the Philippine Atmospheric, Geophysical, and Astronomical Services Administration (PAGASA) to alert the public to the opportunity of a tropical cyclone entering the USA.
When a storm sign number 1 is raised, it method that a tropical cyclone, along with a tropical despair or tropical hurricane, is expected to affect a particular region within the next 36 hours.
The winds related to the cyclone aren't yet strong sufficient to cause widespread harm, but they may be sufficient to disrupt transportation and different outside sports.
Throughout storm sign number 1, the general public is cautioned to be vigilant and take precautions, which include securing loose items and staying indoors if feasible.
Fishermen are recommended to keep away from going out to sea, and small vessels are cautioned to take refuge. PAGASA issues hurricane signal warnings up to a wide variety of five, with better numbers indicating more intense climate situations.
The warnings are a crucial tool for helping the general public to put together for and stay safe throughout tropical cyclones, which could reason extensive damage and loss of life within the Philippines.
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What does it mean if displacement is negative?
Displacement is negative when an object moves in the negative direction. The initial position will be further in the positive direction than the final position.
Displacement is a term used in physics to describe the change in position of an object with respect to its initial position. In other words, it is the distance and direction between an object's starting point and its end point. To calculate displacement, you need to know the object's starting point and end point. The displacement can be positive or negative, depending on the direction of the movement.
Displacement is a vector quantity, which means that it has both magnitude (the distance between the two points) and direction (the direction from the starting point to the end point). It is often represented by an arrow, with the length of the arrow representing the magnitude of the displacement, and the direction of the arrow representing the direction of the displacement.
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We have is when a sound wave passes from air into
The frequency of sound waves remains the same or is unaffected when sound moves from air into water. The correct option is D
What properties of sound waves are affected when sound moves from air into water?Some properties of sound waves will change when it passes from air to water.
The wave's wavelength will lengthen when it passes through the boundary and enters the water.
Because some sound is reflected by the water's surface, the intensity of sound in the water will be lower than it was in the air.
However, because a crest moves away from the border every time a crest approaches it, the frequency will remain the same.
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Complete question:
What happens to a sound wave as it travels from air into water? (a) Its intensity increases. (b) Its wavelength decreases. (c) Its frequency increases. (d) Its frequency remains the same. (e) Its velocity decreases.
A system containing 1 atm of an ideal gas is doubled in temperature and halved in volume. What is the new pressure? 2 atm 1 atm 0.5 atm 4 atm
The new pressure is 2 atm. So the correct answer is (A).
What is ideal gas law?The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature in Kelvin.
Since the gas is ideal, the number of moles and the gas constant remain constant, so we can write:
[tex]P1V1/T1 = P2V2/T2[/tex]
where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2 and V2 are the final pressure and volume.
We are given that the initial pressure is 1 atm, the final volume is half the initial volume, and the final temperature is double the initial temperature. Since temperature is measured in Kelvin, we need to convert the initial temperature of 273 K to 546 K for the final temperature.
Plugging these values into the equation above, we get:
[tex](1 atm)(V1)/(273 K) = (P2)(V1/2)/(546 K)[/tex]
Simplifying, we get:
[tex]P2 = (1 atm)(273 K)/(V1/2)(546 K)[/tex]
P2 = 2 atm
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when a boxer is moving away from a punch, the force experienced is reduced because
By prolonging contact with the punch, the impact power is lessened. Impulse is the result of the product of the force and the application time.
How does science define force?The word "force" has a clear definition. At this level, calling a force a push or a pull is entirely appropriate. A strength is not a property an object "already has in" or that it "contains."
What is an illustration of force?An acceleration-inducing push is referred to as a force. This can literally mean pushing anything, such as moving a large piece of furniture around a room by pushing on it. It might not be as concrete as pressing the gas pedal on a car.
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A runner is moving at a speed of 8. 8m/s rounds a bend with a radius of 25m
Answer:
Explanation:
To solve this problem, we need to use the formula for centripetal force:
F = (mv^2) / r
Where:
F = centripetal force
m = mass of the object
v = velocity of the object
r = radius of the circular path
Assuming the mass of the runner is 70 kg, we can plug in the given values and solve for the centripetal force:
F = (70 kg)(8.8 m/s)^2 / 25 m
F ≈ 217.6 N
Therefore, the centripetal force required to keep the runner moving in a circular path with a radius of 25 m and a speed of 8.8 m/s is approximately 217.6 N.
Please HURRY
particles q_1 = -8.99uc, q_2 = +5.16uc, and q_3=-89.9uc are in a line. particles q_1 and q_2 are separated by 0.220m and particles q_ 2 and q_3 are separated by 0.330m. what is the net force on particles q_1?
According to the question the net force on particle q1 is [tex]1.45 * 10^-4 N.[/tex]
What is force?Force is an influence that produces a change in the motion, direction, shape, or orientation of an object. It is a vector quantity, meaning it has both magnitude and direction. Force can be derived from different sources, including physical contact, gravity, magnetism, or even electrical fields. Force affects objects by producing acceleration, deceleration, or changes in direction.
The net force on particle q1 is the sum of the forces due to the two other particles. The force on particle q1 due to particle q2 is given by Coulomb's Law:
[tex]F12 = k(q1q2/r12^2)[/tex]
Where k is the Coulomb's Constant, q1 and q2 are the charges of the two particles, and r12 is the distance between them, which is 0.220m.
Similarly, the force on particle q1 due to particle q3 is given by:
[tex]F13 = k(q1q3/r13^2)[/tex]
Where q1 and q3 are the charges of the two particles, and r13 is the distance between them, which is 0.330m.
The net force on particle q1 is then the vector sum of these two forces:
Fnet = F12 + F13
Substituting the values for the charges and distances into Coulomb's Law gives:
[tex]Fnet = (9*10^9)(-(8.99*10^-6)(5.16*10^-6)/(0.22^2)) + (9*10^9)(-(8.99*10^-6)(-89.9*10^-6)/(0.33^2))[/tex]
Simplifying, we get
[tex]Fnet = 1.45 * 10^-4 N[/tex]
Therefore, the net force on particle q1 is[tex]1.45 * 10^-4 N.[/tex]
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An astronaut who fell into a black hole would be stretched be-
a. the gravity is so strong.
b. the gravity changes dramatically over a short distance.
c. time is slower near the event horizon.
d. black holes rotate rapidly, dragging spacetime with them.
An astronaut who fell into black hole would be stretched be : b. the gravity changes dramatically over short distance.
What is meant by black hole?Black hole is a place in space where gravity pulls so much that even light can not get out and the gravity is so strong as the matter has been squeezed into tiny space. This can happen when star is dying. As no light can get out, people can't see black holes and they are invisible.
Black hole is a region of spacetime where gravity is so strong that nothing, including light or electromagnetic waves, has energy to escape its event horizon.
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if the solution exhibits a maximum absorbance at 445 nm from the spectrometer, the color of the solution is mostly
if a solution's maximum absorbance is measured at 445 nm from The hue of the solutions is mostly determined by the visible region of the spectrum Blue
What is the spectrophotometer's maximum absorbance?The useful absorbance range for the majority of spectrometers and colorimeters is between 0.1 and 1. Values of absorbance more than and similar to 1.0 are excessive. Your solution is overly concentrated if the absorbance readings you are getting are 1.0 or higher.
What shade of light has a wavelength between 450 and 500 nm?wavelength From 390 to 500 nm, blue light represents visible light. Blue light is divided into blue-violet light and blue-turquoise light (380–450 nm) (450 to 500 nm). Blue light is around yet another of all visible light.
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Under favorable circumstances, including reaction time, a motor vehicle going 50 mph can be stopped within:A) about 550 feetB) about 229 feetC) about 143 feetD) about 78 feet
A car traveling at 50 mph can be stopped in roughly 229 feet under ideal conditions, including reaction time.
How do you define reaction?When several atoms or molecules with the proper orientation and the least amount of energy efficiently collide, a reaction happens. Rate of reaction are the molecules that commence a chemical change, whereas products are the molecules that are formed as a consequence of the reaction.
Why would reactions occur?Two features of nuclear reactions are the formation of new bonds between carbon molecules in resultant particles and the establishment of molecular links amongst individual atoms (particles) (molecules). The quantity of structures changes despite the fact the number of atoms is the same before and after the chemical transition.
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A skateboarder on a ramp is accelerated by a nonzero net force. For each of the following statements, state whether it is always true, never true, or sometimes true.a. The skateboarder is moving in the direction of the net force.a. Always trueb. Sometimes truec. Never true
The given statement "The skateboarder is moving in the direction of the net force." is , b. Sometimes true.
The acceleration of the skateboarder depends on the net force acting on them and the mass of the skateboarder. The direction of the acceleration is in the same direction as the net force. However, the direction of the skateboarder's b may not always be in the same direction as the net force. For example, if the skateboarder is moving up a ramp, the net force may be acting downward due to gravity, but the skateboarder's motion is still upward. Therefore, statement a is not always true, but it can be true in certain situations.
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What is the frequency of light when the energy for a mole of photons is 1.55 × 10^13 J? a)3.88 × 10^22 Hz b)1.03 × 10^20 Hz c)6.18 × 10^21 Hz d)2.58 x 10^23 Hz
The required frequency of light when the energy for a mole of photons is given is 3.88× 10²² hz. Correct option is A.
We know the relation between energy, planck's constant and frequency as,
E = n h v
where,
E is energy
h is planck's constant
v is frequency
n is number of photons
1 mole = 6.023 × 10²³ number of photons
The energy of mole of photons is given as 1.55 × 10¹³ J.
Putting the values into the equation by making frequency as subject,
v = E/nh = (1.55 × 10¹³)/(6.023 × 10²³ × 6.62 × 10⁻³⁴) = (1.55 × 10¹³)/(39.87×10⁻¹¹) = 0.0388 × 10²⁴ hz = 3.88× 10²² hz
Thus, the frequency of light when the energy for a mole of photons is given is 3.88× 10²² hz.
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Copernicus said that t he rotation of the Earth on its axis caused the A daily motions in the heavens. B phases of the Moon. C retrograde motion of the planets D eclipses of the Moon. E motion of the Sun along the ecliptic.
According to Copernicus, the Earth's rotation on its axis is what causes the daily motions in the heavens.
According to Nicholas Copernicus' (1473–1543) Copernican paradigm, the sun is a stationary body at the centre of the universe, and all other bodies are said to rotate around it. Hence, the daily rising and setting of heavenly bodies are caused by the Earth's rotation on its axis.Copernicus was a Renaissance-era astronomer who proposed that the Earth and other planets revolved around the Sun. This was a revolutionary idea at the time, as most astronomers believed that the Earth was the center of the universe. His theory, known as the heliocentric model, revolutionized the way we think about our place in the universe and helped to usher in the scientific revolution.
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The moon is brightest during which of these events?
a.Total solar eclipse
b.Penumbral lunar eclipse
c.Annular eclipse
d.Total lunar eclipse
The moon is brightest during which of these events b.Penumbral lunar eclipse
What may be seen during a total solar eclipse?
The Sun has now been entirely obscured, showing the full splendor of the solar corona. The corona, the Sun's upper atmosphere, which pours out into space above the sun's surface, is visible only during the few minutes of complete solar eclipse.
The Moon is still visible during totality. Sunlight travelling through the Earth's atmosphere gives an orange or reddish hue on the lunar surface. Despite the lack of direct sunshine, the Moon will be visible at totality, glowing orange or reddish.
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What is a buoyancy in physics?
The buoyant pressure is the upward force a fluid exerts on an item. Archimedes' precept is the fact that buoyant force is identical to the weight of the displaced fluid.
Buoyancy is a physical phenomenon that describes the upward force this is exerted on an item submerged in a fluid, inclusive of water or air. This pressure is a result of the pressure differences between the top and backside of an item in a fluid, and it is referred to as buoyant pressure.
The study of buoyancy is important in various fields, including naval architecture, oceanography, and engineering. For example, understanding buoyancy is crucial for designing ships and submarines that can float and maintain stability in water, as well as for developing buoyancy systems for offshore oil and gas drilling. Buoyancy also plays a key role in meteorology, as it affects the movement of air masses and the formation of clouds and precipitation.
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The distribution of the heights of students in a large class is roughly bell-shaped. Moreover, the average height is 68 inches, and approximately 95% of the heights fall between 63 and 73 inches. State the approximate standard deviation of the height distribution to one place of decimal with no units.
Since approximately 95% of the heights fall between 63 and 73 inches, this means that the range of values within two standard deviations of the mean captures 95% of the data.
What is the average height ?The middle of the range (63, 73), which denotes two standard deviations from the mean, is the mean itself, 68 inches, because the average height is 68 inches. As a result, one standard deviation separates 68 inches from either end of the interval (63 or 73 inches).Therefore, the standard deviation can be roughly expressed as:
(73 - 68) / 1 5 is the standard deviation.
The height distribution's approximate standard deviation, when rounded to one decimal place, is 5 inches. The real standard deviation can be a little bit different from this figure because this approximation relies on the assumption that the height distribution follows a normal distribution.To know more about average height , check out :
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A ball thrown horizontally at 25 m/s travels a horizontal distance of 50 m before hitting the ground.
When a ball is thrown horizontally at 25 m/s, it will travel a horizontal distance of 50 m before hitting the ground.
What is distance?Distance is a measurement of the length between two points. It is measured in a variety of units, such as feet, meters, kilometers, and miles. Distance can also be measured in terms of time, such as hours, minutes, and seconds. Distance can also be measured in terms of speed, such as miles per hour or kilometers per hour.
The time it takes the ball to travel this distance can be determined by dividing the distance (50 m) by the velocity (25 m/s). This would give us a time of 2 seconds. The ball will reach a maximum height at the midpoint of its path, which in this case is 25 m. The ball will reach the ground after 2 seconds and will have no remaining horizontal velocity. The ball's vertical velocity will be zero when it hits the ground.
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When a ball is thrown horizontally we can conclude that the distance from where the ball should be thrown is 19.6m.
What is distance?Distance is a measurement of the length between two points. It is measured in a variety of units, such as feet, meters, kilometers, and miles. Distance can also be measured in terms of time, such as hours, minutes, and seconds. Distance can also be measured in terms of speed, such as miles per hour or kilometers per hour.
The time it takes the ball to travel this distance can be determined by dividing the distance (50 m) by the velocity (25 m/s). This would give us a time of 2 seconds. The ball will reach a maximum height at the midpoint of its path, which in this case is 25 m. The ball will reach the ground after 2 seconds and will have no remaining horizontal velocity. The ball's vertical velocity will be zero when it hits the ground.
Due to that,
At 25 m/s, the ball is thrown horizontally.
50 meters are also the horizontal distance.
Considering the information above,
The hour is
= 50 ÷ 25
= 2 sec
Now
h = 0.5gt²
= 4.9(2)²
= 19.6 m
Therefore, we can infer that 19.6m is the height at which the ball should be hurled.
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Complete question -
A ball thrown horizontally at 25 m/s travels a horizontal distance of 50 m before hitting the ground. From what height was the ball thrown?
A teacher demonstrates air pressure to the class. She takes a soft drink can and puts a little bit of water in it. Then she heats it up until the water is boiling. The students watch as the steam pushes air out of the can. The teacher then quickly takes the can, turns it over and dips the open end in bowl of water. A short time later there is a loud bang and the can collapses.. (a) When the teacher cools the can some of the steam turns back to water. What happens to the air pressure inside the can? (b) Why?( Use ideas about collisions in your answer). (c)Explain why the can collapses.
The can collapses because of the difference in air pressure between the inside and outside of the can and the decrease in air pressure inside the can caused by the condensation of the steam.
What is the significance of the collision of particles?Here when the teacher cools the can, some of the steam turns back into water, and as a result, the air pressure inside the can decreases. The reason for this is due to the collisions as when the steam condenses back into water, due to a decrease in the air pressure,
Hence, the can collapses because of the difference in air pressure between the inside and outside of the can and the decrease in air pressure inside the can caused by the condensation of the steam.
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How does solar energy work? All energy must have a source; what is the source in this case? How do we take the power of the Sun and turn it into usable energy? What can we do with this energy?
a) Solar energy works when the sun shines on a solar panel and the PV cells in the panel absorb the energy from the sunshine.
b) The sun is where solar energy comes from.
c) Photovoltaic (PV) cells, which are found in solar panels, are used to collect solar energy and convert it into usable electricity.
d) A variety of appliances may utilize solar energy, and it can be used to generate power.
Photovoltaic (PV) cells, which are found in solar panels, are used to collect solar energy and convert it into usable electricity.
As sunlight reaches the PV cells, it generates an electric field that flows as electricity.
This electricity may be used to power homes, businesses, and other electrical devices, as well as be stored in batteries for later use. The two main types of solar energy systems are photovoltaic and solar thermal.
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is it illegal to have air fresheners on your rearview mirror?
What is the ratio of the fraction of helium atoms that have a speed between 999 m/s m / s and 1001 m/s m / s to the fraction of neon atoms in the same range of speeds?
The ratio of the fraction of helium atoms that have a speed between 999 m/s and 1001 m/s to the fraction of neon atoms in the same range of speeds can be calculated using the Maxwell-Boltzmann distribution function. The Maxwell-Boltzmann distribution function is given by:
[tex]f(v) = (m / 2πkT)^(3/2) * 4πv^2 * e^(-(mv^2) / (2kT))[/tex]
Where m is the mass of the gas molecule, k is the Boltzmann constant, T is the temperature, and v is the speed of the gas molecule.
To find the fraction of helium atoms that have a speed between 999 m/s and 1001 m/s, we need to integrate the Maxwell-Boltzmann distribution function from 999 m/s to 1001 m/s with respect to v:
[tex]∫_(999)^(1001) f(v) dv[/tex]
Similarly, to find the fraction of neon atoms that have a speed between 999 m/s and 1001 m/s, we need to integrate the Maxwell-Boltzmann distribution function from 999 m/s to 1001 m/s with respect to v, but with the mass of neon instead of the mass of helium:
[tex]∫_(999)^(1001) f(v) dv[/tex]
The ratio of the fraction of helium atoms that have a speed between 999 m/s and 1001 m/s to the fraction of neon atoms in the same range of speeds is then given by:
[tex](∫_(999)^(1001) f(v) dv) / (∫_(999)^(1001) f(v) dv)[/tex]
Where the first integral is with respect to the mass of helium and the second integral is with respect to the mass of neon.
Without knowing the values of the mass of helium, the mass of neon, the Boltzmann constant, and the temperature, we cannot calculate the exact value of the ratio. However, we can say that the ratio will be smaller than 1, since the mass of neon is greater than the mass of helium and the Maxwell-Boltzmann distribution function is inversely proportional to the mass of the gas molecule.
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