Chapter 3

A pendulum swings back and forth, reaching a maximum angle of 45 degrees from the vertical. Which arrow shows the direction of the pendulum bob's acceleration as it moves from left to right through point Q (the low point of the motion)?

#2 (straight up)

A pendulum swings back and forth, reaching a maximum angle of 45 degrees from the vertical. Which arrow shows the direction of the pendulum bob's acceleration at P (the far left point of the motion)?

#3 (down and to the right)

A projectile is fired with an initial speed of 30 m/s at an angle of 60 degrees above the horizontal. The object hits the ground 7.5 s later. (A) How much higher or lower is the launch point relative to the point where the projectile hits the ground? (B) To what maximum height above the launch point does the projectile rise?

(A) -81.05 m (B) s = 34.4 m

During a storm, a car traveling on a level horizontal road comes upon a bridge that has washed out. The driver must get to the other side, so he decides to try leaping the river with his car. The side of the road the car is on the 21.3 m above the river, while the opposite side is only 1.8 m above the river. The river itself is a raging torrent 48.0 m wide. (A) How fast should the car be traveling at the time it leaves the road in order to just clear the river and land safely on the opposite side? (B) What is the speed of the car just before it lands on the other side?

(A) Vxi = 24.1 m.s (B) Vf = 31 m/s

A Ferris wheel with radius 14.0 m is turning about a horizontal axis through its center. The linear speed of a passenger on the rim is constant and equal to 6.00 m/s. What are the magnitude and direction of the passenger's acceleration as she passes through (A) The lowest point in her circular motion (B) The highest point in her circular motion (C) How much time does it take the Ferris wheel to make one revolution?

(A) a = 2.57 m/s^2 upward (B) a = 2.57 m/s^2 downward (C) t = 14.66 s

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by v(t) = [5.00 m/s-(0.0180 m/s^4)t^3]i+[2.00 m/s+(0.550 m/s^2)t]j. (A) What are ax(t) and ay(t), the x- and y-components of the car's velocity as functions of time? (B) What are the magnitude and direction of the car's velocity at t = 8.00 s? (C) What are the magnitude and direction of the car's acceleration at t = 8.00 s?

(A) ax = (-0.036a, m/s^3)t and ay = 0.55 m/s^2 (B) Magnitude: |v|t=8 = 7.47 m/s Direction: 59 degrees (C) Magnitude: |a|t=8 = 0.621 m/s^2 Direction: -62.4 degrees = 297.6 degrees

A "moving sidewalk" in an airport terminal moves at 1.0 m/s and is 35.0 m long. If a women steps on at one end and walks at 1.5 m/s relative to the moving sidewalk, how much time does it take to reach the opposite end if she walks (A) In the same direction the sidewalk is moving? (B) In the opposite direction?

(A) moving in the same direction of the sidewalk in 14 seconds (B) Moving in the opposite direction of the sidewalk is 70 seconds

A boy throws a rock with an initial velocity of 2.15 m/s at 30.0 degrees above the horizontal. If air resistance is negligible, how long does it take for the rock to reach the maximum height of its trajectory?

0.110 s

The pilot of a light airplane with an airspeed of 100 km/h wants to fly due west. There is a strong wind of 120 km/h blowing from the north. If the pilot points the nose of the airplane north of west so that her ground track is due west, what will be her ground speed?

160 km/h

A 100-g ball rolls off a table and lands 2.0 m from the base of the table. A 200-g ball rolls off the same table with the same speed. It lands at distance:

2.0 m

An electrical motor spins at a constant 2857.0 rev/min. If the armature radius is 2.685 cm, what is the acceleration of the outer edge of the armature?

2403 m/s^2

Some plants disperse their seeds when the fruit splits and contracts, propelling the seeds through the air. The trajectory of these seeds can be determined with a high-speed camera. In an experiment on one type of plant, seeds are projected at 20 cm above ground level with initial speeds between 2.3 m/s and 4.6 m/s. The launch angle is measured from the horizontal, with +90∘ corresponding to an initial velocity straight up and -90∘ straight down. The experiment is designed so that the seeds move no more than 0.20 mm between photographic frames. What minimum frame rate for the high-speed camera is needed to achieve this?

25,000

A rock is thrown at a window that is located 18.0 m above the ground. The rock is thrown at an angle of 40.0 degrees above horizontal. The rock is thrown from a height of 2.00 m above the ground with a speed of 30.0 m/s and experiences no appreciable air resistance. If the rock strikes the window on its upward trajectory, from what horizontal distance from the window was it released?

27.3

An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the origination of the flight. The plane flies with an air speed of 120 m/s. If a constant wind blows at 10.0 m/s due west during the flight, what direction must the plane fly relative to north to arrive at the destination?

4.78 degrees east of north

A factory conveyor belt at 3 m/s. A mouse, on the belt, sees a piece of cheese directly across the belt and heads straight for the cheese at 4 m/s. What is the mouse's speed relative to the factory floor while on the belt?

5 m/s

A plane flies directly between two cities, A and B, which are separated by 2300 mi. From A to B, the plane flies into a 65 mi/h headwind. On the return trip from B to A, the wind velocity is unchanged. The trip from B to A takes 65 min less than the trip from A to B. What is the airspeed of the plane, assuming it is the same in both directions?

530 mi/h

A rescue plane flying horizontally at 72.6 m/s spots a survivor in the ocean 182 m directly below and releases an emergency kit with a parachute. Because of the shape of the parachute, it experiences insignificant horizontal air resistance. If the kit descends with a constant vertical acceleration of 5.82 m/s, how far away from the survivor will it hit the waves?

574 m

An object has a position given by r = [2.0 m+(5.00 m/s)t]+[3.0 m/s^2)t^2]j, where quantities are in SI units. What is the speed of the object at time t = 2.00 s?

9.43 m/s

A football player kicks a football in a field goal attempt. When the football reaches its maximum height, what is the relationship between the direction of the velocity and acceleration vectors? Assume air resistance is negligible.

At the maximum height, the velocity and acceleration vectors are perpendicular to each other.

A car is traveling around a curve at a steady 45 mph. Which vector shows the direction of the car's acceleration?

B

A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance, when the package hits the ground the horizontal location of the plane will

Be over the package

A cart that is rolling at constant acceleration on a level table fires a ball straight up. When the ball comes back down, will it land

Behind the launching tube

In which of the these situations would the average velocity over an internal be equal to the instantaneous velocity at the end of the interval?

Body moving along a straight line at constant speed

A cart that is rolling at constant velocity on a level table fires a ball straight up. When the ball comes back down, will it land

Directly in the tube

You toss a ball, in the positive direction. The ball falls freely under the influence of gravity. At the highest point in the ball's motion,

Its velocity is zero and its acceleration is negative (downward)

If an objects travels at a constant speed in a circular path, the acceleration of the object is

Larger in magnitude the smaller the radius of the circle

A projectile is launched at a 30 degree angle above the horizontal. Ignore air resistance. The projectile's acceleration is greatest:

Misleading question - the acceleration is the same (but nonzero) at all points along the trajectory

Our balance is maintained, at least in part, by the endolymph fluid in the inner ear. Spinning displaces this fluid, causing dizziness. Suppose a dancer (or skater) is spinning at a very fast 3.0 revolutions per second about a vertical axis through the center of his head. Although the distance varies from person to person, the inner ear is approximately 7.0 cm from the axis of spin What is the radial acceleration (in m/s^2) of the endolymph fluid? Express your answer in meters per second squared. What is the radial acceleration (in g's) of the endolymph fluid? Express your answer as a multiple of g.

arad = 25 m/s^2 a = 2.5 g

Two particles, A and B, are in uniform circular motion about a common center. The acceleration of particle A is 8.5 times that of particle B. The period of particle B is 2.0 times the period of particle A. The ratio of the radius of the motion of particle A to that of particle B is closest to

rA/rB = 2.1

Alice and Tom dive from an overhang into the lake below. Tom simply drops straight down from the edge, but Alice takes a running start and jumps with an initial horizontal velocity of 25 m/s. Neither person experiences any significant air resistance. Just as they reach the lake below

the speed of Alice is larger than that of Tom

Canada geese migrate essentially along a north-south direction for well over a thousand kilometers in some cases, traveling at speeds up to about 100 km/h. The one goose is flying at 100 km/h relative to the air but a 40 km/h wind is blowing from west to east. At what angle relative to the north-south direction should this bird head to travel directly southward relative to the ground? Express your answer in degrees. How long will it take the goose to cover a ground distance of 400 km from north to south? (Note: Even on cloudy nights, many birds can navigate using the earth's magnetic field to fix the north-south direction.) Express your answer in hours.

theta = 24 degrees west of south t = 4.4 h

An object is projected with initial speed v0 from the edge of the roof of a building that has height H. The initial velocity of the object makes an angle α0 with the horizontal. Neglect air resistance. If α0 is 90∘, so that the object is thrown straight up (but misses the roof on the way down), what is the speed v of the object just before it strikes the ground? Express your answer in terms of some or all of the variables v0, H, and the acceleration due to gravity g. If α0 = -90∘, so that the object is thrown straight down, what is its speed just before it strikes the ground? Express your answer in terms of some or all of the variables v0, H, and the acceleration due to gravity g. Derive an expression for the speed v of the object just before it strikes the ground for general α0. Express your answer in terms of some or all of the variables v0, α0, H, and the acceleration due to gravity g. The final speed v equals v1 when α0 equals α1. If α0 is increased, does v increase, decrease, or stay the same?

v = sqrt(v0^2 + 2gH) v = sqrt(v0^2 + 2gH) v = sqrt(v0^2 + 2gH) v stays the same

A cannon, located 60.0 m from the base of a vertical 25.0-m-tall cliff, shoots a 15 kg shell at 43.0∘ above the horizontal toward the cliff. What must the minimum muzzle velocity be for the shell to clear the top of the cliff? Express your answer with the appropriate units. The ground at the top of the cliff is level, with a constant elevation of 25.0 m above the cannon. Under the conditions of part A, how far does the shell land past the edge of the cliff? Express your answer with the appropriate units.

v0, min = 32.6 m/s L = 0 m

The coordinates of a bird flying in the xy plane are given by x(t)=αt and y(t) = 3.0m − βt^2, where α = 2.4m/s and β = 1.2 m/s^2. Calculate the velocity vector of the bird as a function of time. Express your answers in meters per second in terms of t separated by a comma. Calculate the acceleration vector of the bird as a function of time. Express your answers in meters per second squared in terms of t separated by a comma. Calculate the magnitude of the bird's velocity at t=2.0 s. Express your answer in meters per second. Let the direction be the angle that the vector makes with the +x axis measured counterclockwise. Calculate the direction of the bird's velocity at t = 2.0 s Calculate the magnitude of the bird's acceleration at t=2.0 s. Express your answer in meters per second squared. Calculate the direction of the bird's acceleration at t=2.0 s. Express your answer in degrees. At t=2.0 s, is the bird speeding up, slowing down or moving at constant speed?

vx, vy = 2.4, -2.4t m/s ax, ay = 0, -2.4 m/s^2 v = 5.4 m/s theta = -63 degrees 2.4 m/s^2 theta = 270 degrees speeding up

A rhinoceros is at the origin of coordinates at time t1 = 0. For the time interval from t1 to t2 = 14.5 s, the rhino's average velocity has x-component -3.70 m/s and y-component 4.20 m/s. At time t2 = 14.5 s what is the x-coordinate of the rhino? Express your answer in meters. At time t2 = 14.5 s what is the y-coordinate of the rhino? Express your answer in meters. How far is the rhino from the origin? Express your answer in meters.

x = -53.7 m y = 60.9 m r = 81.2 m

The motion diagram shows an object moving along a curved path at constant speed. At which of the points A, C, and E does the object have zero acceleration?

Point C only

Projectile 1 and 2 are launched over level ground with the same speed but at different angles. Which hits the ground first? Ignore air resistance.

Projectile 2 hits first

An object is dropped from an airplane flying at a constant speed in a straight line at a constant altitude. If there is no air resistance, the falling object will (as seen from the ground)

Remain directly under the airplane

At what angle, above the horizon, should a cannon be fired in order for the cannon ball to obtain the greatest horizontal range? Assume air resistance is negligible.

The cannon should be fired at an angle of 45° above the horizon.

For a projectile launched horizontally, which of the following best describes the downward component of a projectile's velocity? Assume air resistance is negligible.

The downward component of the projectile's velocity continually increases.

For general projectile motion, which of the following best describes the horizontal component of a projectile's acceleration? Assume air resistance is negligible.

The horizontal component of a projectile's acceleration is zero.

For general projectile motion, which of the following best describes the horizontal component of a projectile's velocity? Assume air resistance is negligible.

The horizontal component of a projectile's velocity remains a nonzero constant.

While an object is in projectile motion (with upward being positive) with no air resistance,

The horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to -g

For a projectile launched horizontally, which of the following best describes the horizontal component of a projectile's velocity? Assume air resistance is negligible.

The horizontal component of the projectile's velocity remains a nonzero constant.

The position of an object moving along the x-axis is given by x = 5.0 m-(4.0 m/s)t+(2.0 m/s^2)t^2. Which statement about this object is correct?

The object is at rest at t = 1.0 s

A pilot releases a package from a plane flying horizontally at a constant speed. When the package reaches the ground below, what is the horizontal location of the plane with respect to the package? Assume air resistance is negligible.

The plane will be located directly above the package.

A player kicks a soccer ball in a high arc toward the opponent's goal. When the soccer ball reaches its maximum height, how does its speed at this point compare to its initial speed? Assume air resistance is negligible.

The speed at its highest point is less than its initial speed.

A swimmer is determined to cross a river that flows due south with a strong current. Initially, the swimmer is on the west bank desiring to reach a camp directly across the river on the opposite bank. In which direction should the swimmer head?

The swimmer should swim northeast.

A red water balloon is thrown horizontally from the top of a bridge. At the same instant, a yellow water balloon is dropped off the bridge from the same height. Compare the time of fall for the two balloons. Assume air resistance is negligible.

The two balloons hit the ground at the same time.

An object moves in a circular path at a constant speed. What is the relationship between the directions of the object's velocity and acceleration vectors?

The velocity and acceleration vectors are perpendicular.

For general projectile motion, which of the following best describes the vertical component of a projectile's acceleration? Assume air resistance is negligible.

The vertical component of a projectile's acceleration remains a nonzero constant.

A heavy red ball is released from rest 2.0 m above a flat, horizontal surface. At exactly the same instant, a yellow ball with the same mass is fired horizontally at 3.0 m/s. Which ball hits the ground first?

They hit at the same time

Jan and Len throw identical rocks off a tall building at the same time. The ground near the building is flat. Jan throws her rock straight downward. Len throws his rock downward and outward such that the angle between the initial velocity of the rock and the horizon is 30°. Len throws the rock with a speed twice that of Jan's rock. If air resistance is negligible, which rock hits the ground first?

They hit at the same time

Projectile 1 and 2 are launched over level ground with the different. Both reach the same height. Which hits the ground first? Ignore air resistance.

They hit at the same time

True or False: For an object in uniform circular motion, its velocity and acceleration vectors are always perpendicular to each other at every point in the path.

True

A car comes to a bridge during a storm and finds the bridge washed out. The driver must get to the other side, so he decides to try leaping it with his car. The side the car is on is 21.2 m above the river, whereas the opposite side is a mere 1.5 m above the river. The river itself is a raging torrent 55.0 m wide. How fast should the car be traveling just as it leaves the cliff in order to just clear the river and land safely on the opposite side? Express your answer in meters per second. What is the speed of the car just before it lands safely on the other side? Express your answer in meters per second.

V0 = 27.4 m/s v = 33.7 m/s

On level ground a shell is fired with an initial velocity of 30.0 m/s at 65.0 ∘ above the horizontal and feels no appreciable air resistance. Find the horizontal and vertical components of the shell's initial velocity. Express your answers in meters per second separated by a comma. How long does it take the shell to reach its highest point? Express your answer with the appropriate units. Find its maximum height above the ground. Express your answer with the appropriate units. How far from its firing point does the shell land? Express your answer with the appropriate units. At its highest point, find the horizontal and vertical components of its acceleration. Express your answers in meters per second squared separated by a comma. At its highest point, find the horizontal and vertical components of its velocity. Express your answers in meters per second separated by a comma.

V0h, V0v = 12.7, 27.2 m/s t = 2.77 s hmax = 37.7 m l = 70.4 m ah, av = 0, -9.80 m/s^2 vh, uv = 12.7, 0 m/s

A bicyclist starts at point P and travels around a triangular path that takes her through points Q and R before returning to point P. What is the magnitude of her net displacement for the entire round trip?

Zero

The position of an object moving along the x-axis is given by x = 5.0 m-(4.0 m/s)t+(2.0 m/s^2)t^2. How many times does this object pass through the point x = 0?

Zero

A 2.7 kg ball is thrown upward with an initial speed of 20.0 m/s from the edge of a 45.0-m-high cliff. At the instant the ball is thrown, a woman starts running away from the base of the cliff with a constant speed of 6.00 m/s. The woman runs in a straight line on level ground. Ignore air resistance on the ball. At what angle above the horizontal should the ball be thrown so that the runner will catch it just before it hits the ground? Express your answer in degrees. How far does the woman run before she catches the ball? Express your answer with the appropriate units.

a = 72.5 degrees L = 33.3 m

You want to swim straight across a river that is 76 m wide. You find that you can do this if you swim at an angle of θ = 28 degrees from the upstream direction at a constant rate of 1.5 m/s relative to the water. At what rate does the river flow? The angle θ is measured from the river bank (directly upstream is θ = 0 degrees while directly across the river is θ = 90 degrees).

1.3 m/s

A plane has an eastward heading at a speed of 156 m/s (relative to the air). A 20.0 m/s wind is blowing southward while the plane is flying. The velocity of the plane relative to the ground is

157 m/s at an angle 7.31 degrees south of east

A monkey is sitting at the top of a tree 20 m above ground level. A person standing on the ground wants to feed the monkey. He uses a bow and arrow to launch the food to the monkey. If the person knows that the monkey is going to drop from the tree at the same instant that the person launches the food, how should the person aim the arrow containing the food? Air resistance is small enough to be ignored.

He should aim it at the monkey