Physics Final Pt.1
You work at a garden store for the summer. You lift a bag of fertilizer with a force of 141 N, and it moves upward with an acceleration of 0.815 m/s2. (a) What is the mass (in kg) of the fertilizer bag? (b) How much (in N) does the fertilizer bag weigh?
--------
Tom and his little sister are enjoying an afternoon at the ice rink. They playfully place their hands together and push against each other. Tom's mass is 76 kg and his little sister's mass is 15 kg. If the sister's acceleration is 2.8 m/s2 in magnitude, what is the magnitude of Tom's acceleration?
0.553 m/s^2
A father fashions a swing for his kids out of a long rope that he fastens to the limb of a tall tree. As one of the kids swings from this rope that is 6.60 m long his tangential speed at the bottom of the swing is 8.70 m/s. What is his angular speed in rad/s?
1.32 rad/s
A runner taking part in the 200 m dash must run around the end of a track that has a circular arc with a radius of curvature of 35 m. If he completes the 200 m dash in 24.0 s and runs at constant speed throughout the race, what is the magnitude of his centripetal acceleration (in m/s2) as he runs the curved portion of the track?
1.98 m/s^2
A ship sets sail from Rotterdam, The Netherlands, heading due north at 9.00 m/s relative to the water. The local ocean current is 1.52 m/s in a direction 40° north of east. What is the velocity of the ship relative to the earth?
10.05 m/s 83.4* N of E
A book of mass 9 kg rests on a plank. You tilt one end of the plank and slowly increase the angle of the tilt. The coefficient of static friction between the book and the plank is 0.22. What is the maximum angle of tilt for which the book will remain stationary and not slide down the plank?
12.41*
A rescue helicopter is hovering over a person whose boat has sunk. One of the rescuers throws a life preserver straight down to the victim with an initial velocity of 1.12 m/s and observes that it takes 1.9 s to reach the water. How high (in m) above the water was the preserver released? Note that the downdraft of the helicopter reduces the effects of air resistance on the falling life preserver, so that an acceleration equal to that of gravity is reasonable.
19.82 m
A football is kicked from ground level with an initial velocity of 23.4 m/s at angle of 30.0° above the horizontal. How long, in seconds, is the football in the air before it hits the ground? Ignore air resistance.
2.39 s
With the ability to measure the motion of land masses, continental drift has become an established fact. The North American and European continents are drifting apart at a rate of about 3 cm/yr. At this rate how long will it take them to drift 825 km further apart than at present?
2.75e7 yr
A rotating space station is said to create "artificial gravity"—a loosely-defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. If the space station is 220 m in diameter, what angular velocity would produce an "artificial gravity" of 9.80 m/s2 at the rim?
2.85 rpm
A passenger on a moving train walks at a speed of 2.00 m/s due north relative to the train. The passenger's speed with respect to the ground is 4.5 m/s at an angle of 36.0° west of north. What are the magnitude and direction of the velocity of the train relative to the ground?
Magnitude= 3.12 m/s Direction= 58.25* west of north
An inflatable raft (unoccupied) floats down a river at an approximately constant speed of 5.1 m/s. A child on a bridge, 81 m above the river, sees the raft in the river below and attempts to drop a small stone onto the raft. The child releases the stone from rest. In order for the stone to hit the raft, what must be the horizontal distance between the raft and the bridge when the child releases the stone?
20.74 m
In lacrosse, a ball is thrown from a net on the end of a stick by rotating the stick and forearm about the elbow. If the angular velocity of the ball about the elbow joint is 25.0 rad/s and the ball is 1.10 m from the elbow joint, what is the velocity of the ball?
27.5 m/s
A race car completes a lap on a 1600 m long track with an average speed of 250 km/h. If the car's average speed on the first half of the track was 225 km/h, what was its average speed on the second half?
281.69 km/h
An object of mass 0.77 kg is initially at rest. When a force acts on it for 2.9 ms it acquires a speed of 11.3 m/s. Find the magnitude (in N) of the average force acting on the object during the 2.9 ms time interval.
3000 N
The block in the figure below has a mass of 6.0 kg and it rests on an incline of angle 𝜃. You then push on the block with a force of F = 34 N, directed up the slope as shown. Assume the incline is smooth and determine the angle of the incline if the block moves with constant speed.
35.3*
You are walking around your neighborhood and you see a child on top of a roof of a building kick a soccer ball. The soccer ball is kicked at 33° from the edge of the building with an initial velocity of 19 m/s and lands 65 meters away from the wall. How tall is the building that the child is standing on?
39.35 m
A cheetah can accelerate from rest to a speed of 21.5 m/s in 5.25 s. What is its acceleration (in m/s2)?
4.1 m/s^2
A bicycle tire of radius 0.44 m has a piece of gum stuck on its rim. What is the angle through which the tire rotates when the gum has moved through a linear distance of 1.85 m? Express your answer in radians and degrees.
4.21 rad; 241*
A high fountain of water is located at the center of a circular pool as shown in the figure below. Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be 21.0 m. Next, the student stands at the edge of the pool and uses a protractor to gauge the angle of elevation at the bottom of the fountain to be 55.0°. How high is the fountain?
4.78 m
One end of a rope is tied to a block of mass 3.1 kg and you pull straight up on the other end of the rope to lift the block up off of the ground with an acceleration of 3.3 m/s2. What force (in N) does the rope exert on the block?
40.61 N
A tennis player serves a tennis ball such that it is moving horizontally when it leaves the racquet. When the ball travels a horizontal distance of 14 m, it has dropped 49 cm from its original height when it left the racquet. What was the initial speed, in m/s, of the tennis ball? (Neglect air resistance.)
44.304 m/s
Four forces act on an object, given by A = 40 N east, B = 50 N north, C = 70 N west, and D = 90 N south. What is the magnitude of the net force on the object?
50 N
A 7 kg block is placed on a ramp with a 25 deg angle as shown. What is the normal force on the block?
62.2 N
A rope is run through a frictionless pulley and then attached to a 7 kg block as shown. The other end of the rope is then pulled at a 45 deg angle to keep the block suspended in the air. What force, F, is required to keep the block suspended motionless?
68.6 N
In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines: 2.5 km 45° north of west; then4.70 km 60° south of east; then 5.1 km straight east; then 7.2 km 55° south of west; and finally 2.8 km 5° north of east. What is his final position relative to the island?
9.05 km 61.36* South of East
A truck with 0.340 m radius tires travels at 32.5 m/s. At how many radians per second are the tires rotating? What is this value in rpm?
95.588 rad/s; 913.26 rpm
A sailor drops a wrench from the top of a sailboat's vertical mast while the boat is moving rapidly and steadily straight forward. Where will the wrench hit the deck? ahead of the base of the mast at the base of the mast behind the base of the mast on the windward side of the base of the mast None of the above choices are correct.
At the base of the mast
A flea jumps by exerting a force of 1.32 10-5 N straight down on the ground. A breeze blowing on the flea parallel to the ground exerts a force of 1.18 10-6 N on the flea. Find the direction and magnitude (in m/s2) of the acceleration of the flea if its mass is 6.0 10-7 kg. (Let us assume that Fwind points to the right. We will consider this to be the +x direction and vertical to be the +y direction.)
Magnitude= 12.2 m/s^2 Direction= 9.2* clockwise from vertical
If you toss a ball straight up into the air, what is the direction of the ball's acceleration when it is at its maximum height? Up down The acceleration is zero
DOWN
You promised your younger brother that you would give him a ride on his sled. You first push him from behind with a force of magnitude F1 directed downward at an angle of 25° below the horizontal. After a while you decide to pull him with a force of magnitude F2 directed upward at the same angle above the horizontal. In both cases the sled moves with the same acceleration and friction is negligible. Which of the following statements is true regarding the two forces you used? F1 = F2 F1 > F2 F1 < F2 not enough information
F1=F2
A spaceship is traveling through deep space to a space station and needs to make a course correction to go around a nebula. The captain orders the ship to travel 1.3 106 kilometers before turning 70° and traveling 1.9 106 kilometers to reach the space station. If the captain had not ordered a course correction, what would have been the magnitude and direction of the path of the spaceship if it had traveled to the space station through the nebula?
Magnitude= 2.65e6 km Direction= 42.71 *counterclockwise from +x axis
A truck loaded with sand accelerates along a highway. The driving force on the truck remains constant. What happens to the acceleration of the truck as its trailer leaks sand at a constant rate through a hole in its bottom? - It increases and then decreases. - It decreases at a steady rate. - It decreases and then increases. - It increases at a steady rate. - It remains constant.
It increases at a steady rate.
A baseball is thrown from the outfield toward the catcher. When the ball reaches its highest point, which statement is true? - Its velocity is not zero, but its acceleration is zero. - Its velocity and its acceleration are both zero. - Its velocity is perpendicular to its acceleration. - Its acceleration depends on the angle at which the ball was thrown. - None of the above statements are true.
Its velocity is perpendicular to its acceleration.
A passenger on a moving train walks at a speed of 1.90 m/s due north relative to the train. The train is traveling at 3.5 m/s due east relative to the ground. What are the magnitude and direction of the velocity of the passenger relative to the ground?
Magnitude= 3.98 m/s Direction= 28.5* north of east
The x-component of vector R is Rx = −22.8 units and its y-component is Ry = 31.6 units. What are its magnitude and direction? Give the direction as an angle measured counterclockwise from the +x-direction.
Magnitude= 38.97 units Direction= 125.8 *counterclockwise fromt +x axis
A plane lands on a runway with a speed of 105 m/s, moving east, and it slows to a stop in 15.0 s. What is the magnitude (in m/s2) and direction of the plane's average acceleration during this time interval?
Magnitude= 7 m/s^2 Direction= due west
Two forces P and Q act on an object of mass 16.0 kg with Q being the larger of the two forces. When both forces are directed to the left, the magnitude of the acceleration of the object is 0.800 m/s2. However, when the force P is directed to the left and the force Q is directed to the right, the object has an acceleration of 0.400 m/s2 to the right. Find the magnitudes of the two forces P and Q in newtons.
P= 3.2 N Q= 9.6 N
A student throws a heavy red ball horizontally from a balcony of a tall building with an initial speed v0. At the same time, a second student drops a lighter blue ball from the same balcony. Neglecting air resistance, which statement is true? - The blue ball reaches the ground first. - The balls reach the ground at the same instant. - The red ball reaches the ground first. - Both balls hit the ground with the same speed. - None of the above statements is true.
The balls reach the ground at the same instant.
Which of the following statements is/are correct? - The instantaneous speed is always equal to the magnitude of instantaneous velocity. - The average speed is always equal to the magnitude of average velocity. - Neither of these statements is correct. - Both of these statements are correct.
The instantaneous speed is always equal to the magnitude of instantaneous velocity.
A truck travels due east for a distance of 2.0 km, turns around and goes due west for 9.5 km, and finally turns around again and travels 3.3 km due east. (a) What is the total distance that the truck travels? (b) What are the magnitude and direction of the truck's displacement?
a. 14.8 km b. magnitude= 4.2 km direction= west
A 79.0 kg person is being pulled away from a burning building as shown in the figure below. (a)Calculate the tension (in N) in the first rope, T1, if the person is momentarily motionless. (Enter the magnitude only.) (b)Calculate the tension (in N) in the second rope, T2, if the person is momentarily motionless. (Enter the magnitude only.)
a. 765 b. 201
Influenced by the gravitational pull of a distant star, the velocity of an asteroid changes from from +20.1 km/s to −19.3 km/s over a period of 1.82 years. (a) What is the total change in the asteroid's velocity? (Indicate the direction with the sign of your answer.) (b) What is the asteroid's average acceleration during this interval? (Indicate the direction with the sign of your answer.)
a. -3.94e4 b. -6.86e-4
Suppose the mass of a fully loaded module in which astronauts take off from the Moon is 14,300 kg. The thrust of its engines is 31,500 N. (Assume that the gravitational acceleration on the Moon is 1.67 m/s2.) (a) Calculate (in m/s2) its magnitude of acceleration in a vertical takeoff from the Moon.
a. 0.533 m/s^2
A swimmer bounces straight up from a diving board and falls feet first into a pool. She starts with a velocity of 3.00 m/s, and her takeoff point is 1.60 m above the pool. (a) How long are her feet in the air? (b) What is her highest point above the board? (c) What is her velocity when her feet hit the water?
a. 0.94 s b. 0.46 m c. -- m/s
A block of mass m1 = 37 kg on a horizontal surface is connected to a mass m2 = 16.9 kg that hangs vertically as shown in the figure below. The two blocks are connected by a string of negligible mass passing over a frictionless pulley. The coefficient of kinetic friction between m1 and the horizontal surface is 0.27. (a) What is the magnitude of the acceleration (in m/s2) of the hanging mass? (b) Determine the magnitude of the tension (in N) in the cord above the hanging mass.
a. 1.26 m/s^2 b. 144.52 N
A commuter backs her car out of her garage with a constant acceleration of 1.20 m/s2. (a) How long does it take her to reach a speed of 2.00 m/s? (b) If she then brakes to a stop in 0.8 s, what is her (constant) deceleration?
a. 1.67 s b. -2.5 m/s^2
At the end of a race a runner decelerates from a velocity of 9.00 m/s at a rate of 0.300 m/s2. (a) How far does she travel in the next 16.0 s? (b) What is her final velocity?
a. 105.6 m b. 4.2 m/s
A woman starts to swim directly across a 2.0-km-wide river. Her speed with respect to the water is 1.5 m/s. The river current carries the woman downstream at a speed of 0.91 m/s. (a) How much time, in seconds, does it take her to cross the river? (b) How far downstream, in meters, will the river carry her by the time she reaches the other side of the river?
a. 1333.3 s b. 1213.3 m
You work at a garden store for the summer, and you lift a 9 kg bag of fertilizer with a force of 215 N. (a) What is the magnitude of the acceleration of the fertilizer bag? (b) How much does the fertilizer bag weigh?
a. 14.09 m/s^2 b. 88.2
Suppose your car was mired deeply in the mud and you wanted to use the method illustrated in the figure below to pull it out. (a) What force would you have to exert perpendicular to the center of a rope to produce a force of 14,500 N on the car if the angle is 𝜃 = 3.60°? (Enter the magnitude only.) (b) Real ropes stretch under such forces. What force would be exerted on the car if the angle increases to 7.00° and you still apply the force found in part (a) to its center? (Enter the magnitude only.)
a. 1820 N b. 7471
A kayak on a lake is moving at a constant speed of 3.1 m/s in a direction 42.7° north of west. After 17 min, find the following. (a) How far west, in kilometers, has the kayak traveled? (b) How far north, in kilometers, has the kayak traveled?
a. 2.326 km b. 2.142 km
A block of mass m1 = 39.2 kg on a horizontal surface is connected to a mass m2 = 13.0 kg that hangs vertically as shown in the figure below. The two blocks are connected by a string of negligible mass passing over a frictionless pulley. Assume that the horizontal surface is smooth. (a) What is the acceleration (in m/s2) of the hanging mass? (Enter the magnitude only.) (b) Determine the tension (in N) in the cord. (Enter the magnitude only.)
a. 2.441 m/s^2 b. 95.69 N
A skier speeds down a smooth ski slope which is at an angle of 𝜃 = 21° with the horizontal. The mass of the skier is 69 kg. Take the downhill direction to be positive and uphill to be negative. (a) What net force (in N) is acting on the skier? (Indicate the direction with the sign of your answer.) (b) What is the acceleration (in m/s2) experienced by the skier? (Indicate the direction with the sign of your answer.) (c) How does the net force experienced by the skier change if the ski slope becomes steeper?
a. 242 N b. 3.51 m/s^2 c. Increases
A spherical raindrop 2.9 mm in diameter falls through a vertical distance of 3600 m. Take the cross-sectional area of a raindrop = 𝜋r2, drag coefficient = 0.45, density of water to be 1000 kg/m3, and density of air to be 1.2 kg/m3. (a) Calculate the speed a spherical raindrop would achieve falling from 3600 m in the absence of air drag. (b) What would its speed be at the end of 3600 m when there is air drag? (Note that the raindrop will reach terminal velocity after falling about 30 m.)
a. 265.63 m/s b. 8.39 m/s
A satellite in outer space is moving at a constant velocity of 20.7 m/s in the +y direction when one of its onboard thruster turns on, causing an acceleration of 0.400 m/s2 in the +x direction. The acceleration lasts for 45.0 s, at which point the thruster turns off. (a) What is the magnitude of the satellite's velocity when the thruster turns off? (b) What is the direction of the satellite's velocity when the thruster turns off? Give your answer as an angle measured counterclockwise from the +x-axis.
a. 27.43 m/s b. 49* counterclockwise from + x axis
Two blocks A and B with mA = 1.1 kg and mB = 0.76 kg are connected by a string of negligible mass. They rest on a frictionless horizontal surface. You pull on block A with a horizontal force of 5.7 N. (a) Find the magnitude of the acceleration (in m/s2) of the blocks. (b) Determine the tension (in N) in the string connecting the two blocks. (c) How will the tension in the string be affected if mA is decreased?
a. 3.065 m/s^2 b. 2.33 N c. ---
In an exciting game, a baseball player manages to safely slide into second base. The mass of the baseball player is 73.7 kg and the coefficient of kinetic friction between the ground and the player is 0.45. (a) Find the magnitude of the frictional force in newtons. (b) It takes the player 1.8 s to come to rest. What was his initial velocity (in m/s)?
a. 325.017 N b. 7.938 m/s
A student drove to the university from her home and noted that the odometer on her car increased by 13.0 km. The trip took 18.0 min. (a) What was her average speed? (b) If the straight-line distance from her home to the university is 10.3 km in a direction 25.0° south of east, what was her average velocity? (c) After spending some time at the university, the student then returned home by the same path. The entire trip, including driving to the university, spending time there and driving back home, took 7 hours 30 minutes. What were her average speed and velocity for the entire trip?
a. 43.33 km/h b. 34.33 km/h (25* S of E) c. Average Speed= 3.47 km/h Average Velocity= 0 km/h
A contestant in a winter games event pushes a 40.0 kg block of ice across a frozen lake as shown in the figure below. The coefficient of static friction is 0.1 and the coefficient of kinetic friction is 0.03. (Assume 𝜃 = 27°.) (a) Calculate the minimum force F (in N) he must exert to get the block moving. (b) What is its acceleration (in m/s2) once it starts to move, if that force is maintained?
a. 46.3 N b. -----
A powerful motorcycle can accelerate from rest to 26.8 m/s (60 mi/h) in only 4.90 s. (a) What is its (constant) acceleration? (b) How far does it travel in that time?
a. 5.47 m/s^2 b. 65.66 m
A pulley and string arrangement is used to connect two objects A and B as shown in the diagram below. Here, mA = 1.70 kg and mB = 6.40 kg. The string connecting the two objects is of negligible mass and the pulley is frictionless. The objects start from rest and move with constant acceleration. (a) What is the magnitude of the acceleration (in m/s2) of each of the objects? (b) What is the magnitude (in N) of the tension in the string? (c) Through what distance (in m) will the two objects move in the first second of motion?
a. 5.69 m/s^2 b. 26.3 N c. 2.845 m
To maintain a constant speed, the force provided by a car's engine must equal the drag force plus the force of friction of the road (the rolling resistance). The density of air is 1.2 kg/m3. (a) What are the drag forces in newtons at 75 km/h and 108 km/h for a Toyota Camry? (Drag area = 0.70 m2 and drag coefficient = 0.28.) at 75 km/h --- at 108 km/h ---- (b) What are the drag forces in newtons at 75 km/h and at 108 km/h for a Hummer H2? (Drag area = 2.44 m2 and drag coefficient = 0.57.) at 75 km/h ----- at 108 km/h ------
a. 51.02 N; 105.84 N b. 362.07 N; 751.03 N
A woman drives a car from one city to another with different constant speeds along the trip. She drives at a speed of 75.0 km/h for 25.0 min, 50.0 km/h for 20.0 min, makes a stop for 35.0 min, then continues at 40.0 km/h for 30.0 min, at which point she reaches her destination. (a) What is the total distance between her starting point and destination (in km)? (b) What is the average speed for the entire trip (in units of km/h)?
a. 67.9 km b. 37.04 km/h
The speed limit on certain interstate highways is 55 miles per hour. (a) What is this in feet per second? (b) How many km/h is this?
a. 80.67 ft/s b. 88.495 km/h
The distance from the center of the earth to the center of the sun is 1.5e8 km. What are the average speed and the average velocity of the earth as it moves from position A to position B over 1/2 a year in the image below? In your calculations, use the fact that there are 365 days in a year. When entering the velocity, use the sign of the value to indicate its direction.
a. Average Speed= 29.86 km/s b. Average Velocity= -18.98 km/s
(a) Suppose that the distance that an object travels (x) is related to time according to the expression x = Bt2. What are the dimensions of B? (In the expressions below, "L" is the length dimension and "T" is the time dimension). L T L2/L L × T2 T2/L L/T2 L/T (b) A distance is related to time according to the expression x = A sin(2𝜋ft), where A and f are constants. Find the dimensions of A. Again, "L" is the length dimension and "T" is the time dimension. [Hint: A trigonometric function appearing in an equation must be dimensionless.] L/T T/L T L × T L
a. L/T^2 b. L
You are helping your friend move a new refrigerator into his kitchen. You apply a horizontal force of 254 N in the negative x direction to try and move the 55 kg refrigerator. The coefficient of static friction is 0.67. (a) How much static frictional force does the floor exert on the refrigerator? Give both magnitude (in N) and direction. b) What maximum force (in N) do you need to apply before the refrigerator starts to move?
a. Magnitude= 254 N Direction= + x axis b. 361.13 N
Consider the 65.0-kg ice skater being pushed by two others shown in the figure below. (a) Find the direction (in degrees counterclockwise from the +x-axis) and magnitude (in N) of F the total force exerted on her by the others, given that the magnitudes F1 and F2 are 24.8 N and 19.0 N, respectively. (Assume F1 points in the positive x direction.) (b) What is her initial acceleration (in m/s2) if she is initially stationary and wearing steel-bladed skates that point in the direction of Ftot? (Assume friction is negligible. Enter the magnitude only.) c) What is her acceleration (in m/s2) assuming she is already moving in the direction of Ftot? (Assume friction is negligible. Enter the magnitude only.)
a. Magnitude= 31.24 N Direction= 37.46* counterclockwise from +x axis b. 0.481 m/s^2 c. 0.481 m/s^2
From the top of a cliff, a person throws a stone straight downward. The initial speed of the stone just after leaving the person's hand is 9.9 m/s. (a) What is the acceleration (magnitude and direction) of the stone while it moves downward, after leaving the person's hand? Is the stone's speed increasing or decreasing? (b) After 0.50 s, how far beneath the top of the cliff is the stone? (Give just the distance fallen, that is, a magnitude.)
a. Magnitude= 9.8 m/s^2 Direction= downward increasing b. 6.175 m
onsider the following equations of motion. v =v0 + at Δx =v0t + 12at2 v2 =v02 + 2aΔx (a) Can the equations above be used in a situation where the acceleration varies with time? (b) Can they be used when the acceleration is zero?
a. No b. Yes
Tom and his little sister are enjoying an afternoon at the ice rink. They playfully place their hands together and push against each other. Tom's mass is 58 kg and his little sister's mass is 15 kg. (a) Which of the following statements is correct? - The force experienced by the sister is less than the force experienced by Tom. - The force experienced by - Tom is less than the force experienced by his sister. - They both experience the same force. (b) Which of the following statements is correct? - Tom's acceleration is more than the sister's acceleration. - They both have the same acceleration. - Tom's acceleration is less than the sister's acceleration.
a. They both have the same force. b. Tom's acceleration is less than the sister's acceleration.
Three boxes, A, B, and C, are placed on a frictionless surface as shown in the diagram below. If you push on box A with a force of 8.25 N, find the contact force (in N) between each pair of boxes. Here mA = 5.85 kg, mB = 3.20 kg, and mC = 1.50 kg.
contact force between A and B = 3.675 N contact force between B and C = 1.173
Mary and her younger brother Alex decide to ride the 17-foot-diameter carousel at the State Fair. Mary sits on one of the horses in the outer section at a distance of 8 feet from the center. Alex decides to play it safe and chooses to sit in the inner section at a distance of 5 feet from the center. (a) What is Mary's angular speed 𝜔M compared to that of Alex's angular speed 𝜔A? Give your answer as a multiple of 𝜔A. (b) What is Mary's tangential speed vM compared to that of Alex's tangential speed vA? Give your answer as a multiple of vA.
wM= 1 wA vM= 1.6 vA
