Vector A has a magnitude of 27 m and
points in a direction 32° above the positive x axis. Vec-
tor B has a magnitude of 35 m and points in a direction
55° below the positive x axis. Sketch the vectors A, B,
and C = A + B. Estimate the magnitude and the
direction angle of from
your
sketch.
Answers
Answer:
The magnitude of the resultant is 55.0 m
The angle of resultant is 18.4° below the x axis
Explanation:
Given that,
Magnitude of vector A = 27 m
Angle = 32° above the x axis
Magnitude of vector B = 35 m
Angle = 35° blow the x axis
We need to calculate the angle between the vectors
Using given angle
[tex]\theta=32-(-55)[/tex]
ptex]\theta=87^{\circ}[/tex]
We need to calculate the sum of vector A and B
Using formula of sum of vector
[tex]C=\sqrt{A^2+B^2+2AB\cos\theta}[/tex]
Put the value into the formula
[tex]C=\sqrt{27^2+35^2+2\times27\times35\cos87}[/tex]
[tex]C=55.0\ m[/tex]
We need to calculate the direction angle
Using formula of angle
[tex]\tan\theta=\dfrac{B\sin\theta}{A+B\cos\theta}[/tex]
Put the value into the formula
[tex]\tan\theta=\dfrac{35\sin87}{27+35\cos87}[/tex]
[tex]\tan\theta=1.21[/tex]
[tex]\theta=\tan^{-1}(1.21)[/tex]
[tex]\theta=50.4[/tex]
We need to calculate the angle of the resultant vector makes with vector A
Using formula of angle
[tex]\phi=32-50.4[/tex]
[tex]\phi=-18.4^{\circ}[/tex]
Negative sign shows that the direction of resultant is below the x axis
Hence, The magnitude of the resultant is 55.0 m
The angle of resultant is 18.4° below the x axis
The magnitude of the sum of the vectors, C, can be obtained using the
parallelogram method.
The magnitude of the resultant vector, C, is approximately 45.3 meters.The direction of the resultant vector, C, is approximately 18.6° below the horizontal.Reasons:
The given parameters are;
Magnitude of vector A = 27 m
The direction of vector A = 32° above the horizontal
Magnitude of vector B = 35 m
The direction of vector B = 55° above the horizontal
By drawing, using the parallelogram resolution of vectors on MS Word, and
taking extension of the resultant in the x and y-direction, we have;
C = A + B = 42.92·i - 14.48·j
The magnitude of the resultant vector is therefore;
|C| = √((42.92 m)² + (14.48 m)²) ≈ 45.3 m
The direction is given as follows;
[tex]\theta = arctan \left(-\dfrac{14.48}{42.92} \right) \approx -18.6^{\circ}[/tex]
Verifying, we get;
Vector A = 27×cos(32°)·i + 27×sin(32°)·j ≈ 22.9·i + 14.31·j
Vector B = 35×cos(-55°)·i + 35×sin(-55°)·j ≈ 20·08·i - 28.67·j
C = A + B = ( 22.9·i + 14.31·j) + (20·08·i - 28.67·j) = 42.98·i - 14.36·j
Therefore, the vector obtained by sketch is correct approximately.
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Related Questions
Please help in my home work.
change 120°F to celsius scale.
Answers
Answer:
48
Explanation:
I'm not sure if this is right I'm so sorry if its not
120 °F
to find:120 Fahrenheit as Celsius.
solution:[tex]c = (f - 32) \times \frac{5}{9} [/tex]
[tex]c = (120 - 32) \times \frac{5}{9} [/tex]
[tex]c = \frac{440}{9} [/tex]
[tex]c = 48.88889 \: degree \: celcius[/tex]
A book with a mass of 1 kg is dropped from a height of 3 m. what is the potential energy of the book when it reaches the floor
Answers
Answer:
PE=mgh
Where; m is the mass
g is the gravitational force.
h is the height.
the mass is 1kg, the acceleration due to gravity has a constant value of 10ms² . And the height is 3m.
mgh= 1 x 10 x 3 = 30Joules
What place on the earth has the highest air pressure? What is it’s elevation and air pressure?
Answers
Answer:
Siberia
Explanation:
The highest sea-level pressure on Earth occurs in Siberia, where the Siberian High often attains a sea-level pressure above 1050 mbar with record highs close to 1085 mbar.
NOTE: mbar = Millibar, the unit of air pressure in the metric system, commonly used in meteorology, equal to 100 pascals, 1,000 dynes per square cm (about 0.0145 pounds per square inch), or slightly less than one-thousandth of a standard atmosphere.
A labourer carries a load of 500N to a distance of 100m
The work done is??
Answers
Explanation:
Hey there!
Given;
Load = 500N
Distance= 100m
Acceleration due to gravity= 9.8m/s^2.
We know;
Work done = F * d
W = (500*9.8)*100
W= 490000J
Therefore, the work done by the carrier is 490000J.
Hope it helps...
What is the equation for the speed of a wave? Identify each variable.
Answers
Answer:
Wave speed is related to wavelength, frequency, and period by the equation wave speed = frequency x wavelength.
Explanation:
I hope my answer helped <3 Have a nice day
The equation for the speed of the wave is v = λ × f. The speed of a wave depends on wavelength and frequency.
The rate at which a wave moves across a medium is referred to as its speed. It displays the speed at which the wave's disruption or energy spreads. The characteristics of the medium a wave travels through affect its speed.
The equation for the wave's speed (v) for a mechanical wave, such as one moving via a string or a spring, is as follows:
v = λ × f
Here:
v = speed of the wave
λ = wavelength of the wave
f = frequency of the wave
Hence, the equation for the speed of the wave is v = λ × f. The speed of a wave depends on wavelength and frequency.
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Please help me I’ll mark you as Brainly
PLSSSS
Answers
Answer:
D
Explanation:
Since Ball X accelerates at 8m/s2, its acceleration will be doubled. A faster acceleration means the least mass.
direction of the sum of the two vectors
Answers
Explanation:
V² = Vx² + Vy²
= [ 9.66 cos (0) ]² + [ 12 cos (135) ]²
= 165.31
V = root 165.31 = 12.85
can you please mark my answer brainliest ♥️...
The direction of the sum of vectors A and B is approximately 22.9 degrees north of east.
To find the direction of the sum of vectors A and B, we can use trigonometry to determine the angle with respect to the positive x-axis (east direction). The given vectors A and B have magnitudes and directions as follows:
Vector A: Magnitude = 9.66 m, Direction = East
Vector B: Magnitude = 12.0 m, Direction = Northwest (which is 45 degrees north of west)
To find the resultant vector's direction, we need to add the angles of the two vectors. The angle between the positive x-axis and vector A is 0 degrees (east direction), and the angle between the positive x-axis and vector B is 45 degrees (northwest direction). Therefore, the angle between vector A and the resultant vector is 0 degrees, and the angle between vector B and the resultant vector is 45 degrees.
To find the angle of the resultant vector with respect to the positive x-axis (east direction), we can use the tangent function:
Tan(Angle)= Opposite/Adjacent = Magnitude of Vector A/Magnitude of Vector B
Taking the inverse tangent (arctan) of both sides:
Angle = arctan (9.66/12.0)≈22.9 degrees
So, the direction of the sum of vectors A and B is approximately 22.9 degrees north of east.
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What happens to the momentum of an object when velocity is kept the same and the mass is increased?
Answers
it took 500 newtons of force to push a car 4meters how much work was done?
Answers
Answer:
The answer is 2000 JExplanation:
The work done by an object can be found by using the formula
workdone = force × distance
From the question we have
workdone = 500 × 4
We have the final answer as
2000 JHope this helps you
What is the velocity of a wave with a length of 10 m and frequency of 5hz.
Answers
The velocity of the wave is defined by the product of wavelength and frequency. The velocity of a wave with a length of 10 m and frequency of 5hz will be 50 m/sec.
What is the velocity of the wave?The velocity of the wave is defined by the product of wavelength and frequency. It is obtained from the formula of the wavelength which is given by;
[tex]\rm \lambda=\frac{v}{f} \\\\ \rm v = \lambda \times f \\\\ \rm v = 10 \times 5 \\\\ \rm v = 50\ m/sec[/tex]
Hence the velocity of a wave with a length of 10 m and frequency of 5hz will be 50 m/sec.
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Four model rockets are launched in a field. The mass of each rocket and the
net force acting on it when it launches are given in the table below.
Rocket
Mass (kg)
Force (N)
1
4. 25
120
2
2
3. 25
120
3
5. 50
120
4
4. 50
120
Which rocket has the highest acceleration?
A. Rocket 3
B. Rocket 1
C. Rocket 4
D. Rocket 2
Answers
In the given four models of rockets, the rocket with the highest acceleration is rocket 2.
Acceleration of the rocketsAcceleration is the rate of change of velocity with time. The acceleration of the rockets can also be determined from Newton's second law of motion with the applied force and mass of each rocket as shown below;
F = ma
where;
F is the applied forcem is the massa is the accelerationa = F/m
Rocket 1a = 120/4.25
a = 28.24 m/s²
Rocket 2a = 120/3.25
a = 36.92 m/s²
Rocket 3a = 120/5.5
a = 21.82 m/s²
Rocket 4a = 120/4.5
a = 26.7 m/s²
Thus, the rocket with the highest acceleration is rocket 2.
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A 35.0- g bullet strikes a 5.0- kg stationary piece of lumber and embeds itself in the wood. The piece of lumber and the bullet fly off together at 8.6 m/s. What was the speed of the bullet before it struck the lumber? Define the bullet and the wood as a system.
please show work , help
Answers
Answer:
1237.17 m/s
Explanation:
Applying the law of conservation of momentum,
m₁v₁ + m₂v₂ = (m₁ + m₂)v0.035v₁ + 0 = 5.035 x 8.60.035v₁ = 43.301v₁ = 43.301/0.035v₁ = 1237.17 m/sYou want the maximum compression of the spring to be 0.31 mm . What must be the force constant of the spring
Answers
Thee force constant can be obtained using the relation, K = F/e
What is Hooke's law?According to Hooke's law, as long as the elastic limit is not exceeded, the extension is directly proportional to the force applied. In this case, the question is incomplete since the force applied is missing.
Now, from Hooke's law;
F = Ke
K = F/e
Hence, if we have the force applied, we can conveniently obtain the force constant of the spring.
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Ahab has been sent to the shops by his mother. The shops are 1200 m from his
home. If Ahab can run at an average speed of 6 m/s, how long will it take him
5
to reach the shops?
Answers
Answer:
it will take him 200secs to run to the shops
(btw 200 seconds is 3minutes and 20secs)
Explanation:
distance = speed x time
time = distance / speed
1200 ÷ 6 = 200
time = 200seconds
hope this helps
brainliest please?
x
Please help me with this I’ll mark you Brainly
The picture is above
Answers
Answer:
D is correct.
The upward force on the ball must be the same at both locations:
F = M a = 0 = F(upwards) - F(downwards)
If the ball is not being accelerated the upward force must equal the downward force on the ball.
__________ is the process of altering light so that the waves are all oscillating in the same plane.
Polarization
Reflection
Diffraction
Refraction
Answers
Polarized sunglasses block the waves in one direction and pass the other plane. Allows us to see objects below the surface of reflected lite coming off water.
Before a diver jumps off of a diving board she has 7500J of Gravitational energy. What is the maximum amount of kinetic energy the diver will have just before she hits the water?
Answers
Answer:
i think it was 7500 j . beacause sometimes we can say that U=K after that thing is near the floor
The maximum amount of kinetic energy the diver will have just before she hits the water will be the same as the gravitational potential energy before take-off. Maximum kinetic energy is also 7500Joules
Gravitational energy is the energy possessed by an object by virtue of its position.
It is expressed according to the formula:
GPE = mgh
m is the mass of the object
g is the acceleration due to gravity
h is the height
If a diver has Gravitational energy of 7500Joules before the diver jumps off, the maximum amount of kinetic energy the diver will have just before she hits the water will be the same as the gravitational potential energy before take-off.
GPE = kinetic energy at the bottom = 7500Joules
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I have two questions
What is the current of a 24 ohm heating coil in a coffee maker plugged into a 120v outlet.
What voltage will produce 6 amps through a circuit that has 10 ohms of resistance.
plz help
Answers
Voltage = current x resistance = 6 x 10 = 60 Volts
a) The electric current flowing through it is 5 amp.
b) The voltage will produce by an amount of 60 volt.
What is electric current?A stream of charged particles, such as electrons or ions, travelling through an electrical conductor or a vacuum is known as an electric current. The net rate of electric charge flowing through a surface or into a control volume is how it is calculated.
a) When a 24 ohm heating coil in a coffee maker plugged into a 120v outlet, electric current flowing trough it = 120 v/24 ohm = 5 amp.
b) When e 6 amps through a circuit that has 10 ohms of resistance, voltage produced in it = 6 amp × 10 ohm = 60 volt.
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Find the acceleration of a car with a mass of 1,200 kg and a force of 11,000 N.
Please help
Answers
Answer:
9.17 m/s^2
Explanation:
Formula for force is given by
F = m*a
where F is the force in newton
m is the mass of body in KG
and
a is the acceleration of body on m/s^2
_______________________________________________
Given
F = 11,000
mass = 1,200 Kg
we have to find value of acceleration
using
F = m*a
11,000 = 1200*a
=> a = 11,000 /1200 = 9.17
Thus, the acceleration of a car is 9.17 meter per second square
Sofia needs to go to the grocery store. She leaves her house, walks 1 mi north
to the store, buys some bread and fruit, and walks back home. Which of the
following is true of Sofia's trip to the store and back?
O A. The total distance traveled is 1 mi.
O B. The total distance traveled is O mi.
C. The total displacement is O mi.
D. The total displacement is 1 mi north.
Answers
A, B, and D aren't.
find two rational num between -3 and 2
Answers
Answer:
1 and -2
Explanation:
Basically rational numbers are numbers that can be expressed as a fraction and 1 can be expressed as 1/1 and -2 can be expressed as -2/1.
Raymond cattell created the 16pf self-inventory assessment by first taking 4,504 personality traits and removing all of the __________. a. nouns b. homonyms c. synonyms d. antonyms please select the best answer from the choices provided a b c d
Answers
Raymond Cattell created the 16pf self-inventory assessment by first taking 4,504 personality traits and removing all of the synonyms.
What exactly is a synonym?This is defined as a word or phrase that has a similar meaning to another word or phrase.
By removing synonyms from the personality traits, Raymond Cattell created the 16PF self-inventory assessment.
Hence Raymond Cattell created the 16pf self-inventory assessment by first taking 4,504 personality traits and removing all of the synonyms.
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According to Newton’s law inertia what will happen to the ballon when the force of gravity equals the upward force?
Answers
Answer:
It will stop moving.
The orbital motion of a deep water wave extends to a depth equal to.
Answers
1. Old Faithful is a geyser in Yellowstone National Park. This geyser erupts when hot water from
underground shoots up into the air through an opening in the ground. When this happens, the ground
surrounding the water increases in temperature. What happens to the molecules in the ground when
he temperature increases?
a
More heat molecules combine with the molecules in the ground.
b
The energy of the molecules in the ground decreases.
c
The energy of the molecules in the ground increases.
d
The cold energy of the molecules in the ground decreases.
Please help thanks!!
Answers
Answer:
c
Explanation:
i just did the test
The energy of the molecules in the ground increases in the given case when the temperature increases.
• The heat of the Earth is released in both conduction and convection in Yellowstone Park.
• Conduction takes place when the transferring of heat takes place from something hot to something cold.
• On the other hand, convection takes place when the transferring of heat takes place by the movement of hot gases or liquids like water, air, or magma to a cooler region.
• The same phenomenon takes place underneath the Yellowstone. The convection of the molten rock in the magma chamber underneath transfers heat via the caldera of Yellowstone.
• Near the surface of the ground, the convection of heat water results in the hot springs and geysers in the park.
Thus, when the temperature increases, the energy of the molecules in the ground also increases resulting in the formation of geysers. The correct answer is option c.
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Questions
2.
Rewrite the following quantities using suitable
prefixes
5000 000
Answers
Explanation:
Here,^ represents 6 times 10 and 5 is multiplied. That is 5000 000.
Hope this helps
HELP ME PLEAS AND FASTT
What is the best location for a tidal power plant?
Question 5 options:
A beach.
The ocean.
An inlet or bay.
Answers
A girl cycles for 3hrs at a speed of 40 km/h. What distance did she travel?
Answers
Answer:
120 km
Explanation:
Answer:
120 km
Explanation: 3x40= 120 :)
Which of the following objects has the greatest kinetic energy?
à baseball flying through the air at 90 miles per hour
a baseball flying through the air at 45 miles per hour
O a baseball flying through the alr at 20 miles per hour
a baseball sitting on the ground
Answers
Answer:
A. a baseball flying through the air at 90 miles per hour
Explanation:
Kinetic Energy is the energy of mass in motion
hello people ~
During dry weather, while combing hair, sometimes we experience hair flying apart. The force responsible for this is
(a) force of gravity.
(b) electrostatic force.
(c) the force of friction.
(d) magnetic force.
Answers
Answer:
Electrostatic force
Explanation:
When we comb the hair
The comb gets positively charged.The hair got negatively chargedSo they get attracted and share electrons so that because of electrostatic force