Physics I Chapter 2 & 3

A car is initially traveling west at 25 mph, and makes a turn north. As the car finishes the turn, its velocity is 20 mph north. It takes 3.5 seconds to complete the turn. What is the average acceleration of the car while it is turning, in mph/s? Let east be the positive-x direction and north be the positive-y direction.

-7.1 i + 5.7 j

An object moves 10.0 m east in 10.0 s and then returns to its starting point taking an additional 40.0 s. If west is chosen as the positive direction, what is the average speed of the object?

0.4 m/s

Omar throws a rock down with speed 12.5 m/s from the top of a tower. The rock hits the ground after 1.50 s. What is the height of the tower? (air resistance is negligible)​

30.0 m

A rock is thrown straight up with an initial velocity of 25.0 m/s. What maximum height will the rock reach before starting to fall downward? (Take acceleration due to gravity as 9.80 m/s2.)​

31.9 m

A rock, released at rest from the top of a tower, hits the ground after 3.5 s. What is the speed of the rock as it hits the ground? (g = 9.8 m/s2 and air resistance is negligible)

34 m/s

A quarterback takes the ball from the line of scrimmage, runs backward for 12 yards, then sideways parallel to the line of scrimmage for 18 yards. He then throws a 47-yard forward pass straight downfield perpendicular to the line of scrimmage. The receiver is tackled immediately. How far is the football displaced from its original position?

39 yards

Plane A is flying at 440 mph in the northeast direction relative to the Earth. Plane B is flying at 550 mph in the north direction relative to the Earth. What is the speed of Plane B as observed from Plane A?

392 mph

Mt. Everest is more than 8 000 m high. How fast would an object be moving if it could free fall to sea level after being released from an 8 000-m elevation? (Ignore air resistance.)

396 m/s

A boat travels upstream and after one hour has gone 10 km. The boat next travels downstream and after one hour has gone 18 km. If the boat's speed relative to the water is constant, what is the speed of the current in the river?

4 km/h

Maria throws two stones from the top edge of a building with a speed of 22 m/s. She throws one straight down and the other straight up. The first one hits the street in a time t1. How much later is it before the second stone hits?

4.5 s

A river flows due east at 2.0 m/s. A boat crosses the 300-m-wide river by maintaining a constant velocity of 15 m/s due north relative to the water. If no correction is made for the current, how far downstream does the boat move by the time it reaches the far shore?​

40 m

Plane A is flying at 350 mph in the northeast direction relative to the Earth. Plane B is flying at 460 mph in the north direction relative to the Earth. What is the direction of motion of Plane B as observed from Plane A?

40.7° N of W

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 12 m/s. A stop watch measures the stone's trajectory time from top of cliff to bottom to be 4.8 s. What is the height of the cliff? (g = 9.8 m/s2 and air resistance is negligible)

84 m

A projectile is fired at an angle of elevation of 30°. Neglecting air resistance, what are possible angles in flight between the acceleration vector and the velocity vector?

90° and 30°

A string attached to an airborne kite is maintained at an angle of 44.0° with the horizontal. If a total of 160 m of string is reeled in while bringing the kite back to the ground, what is the horizontal displacement of the kite in the process? (Assume the kite string doesn't sag.)

115 m

An object moves at a constant velocity of 12 m/s to the southwest for an interval of 20 s. Halfway through this interval, what is the magnitude of its instantaneous velocity?

12 m/s

A vehicle designed to operate on a drag strip accelerates from zero to 34 m/s while undergoing a straight-line path displacement of 48 m. What is the vehicle's acceleration if its value may be assumed to be constant?

12 m/s2

In which of the following cases is the displacement's magnitude half the distance traveled?​

12 steps east followed by 4 steps west

A startled deer runs 520 m at 20.0° north of east for half a minute, then turns and runs 380 m at 55.0° north of west for 15.0 seconds and stops. What is the average velocity of the deer during this time?

12.4

A jogger runs halfway around a circular path with a radius of 60.0 m. What, respectively, are the magnitude of the displacement and the distance jogged?

120 m, 188 m

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 8.0 m/s. A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.9 s. How far out from the cliff's edge does the stone travel horizontally? (g = 9.8 m/s2 and air resistance is negligible)

130 m

Human reaction time is usually about 0.18 s. If your lab partner holds a ruler between your finger and thumb and releases it without warning, how far can you expect the ruler to fall before you catch it? The nearest value is​

16 cm

A rock is rolled in the sand. It starts at 5.0 m/s, moves in a straight line for a distance of 6.0 m, and then stops. What is the magnitude of the average acceleration?

2.1 m/s2

A boat moves at 10.8 m/s relative to the water. If the boat is in a river where the current is 2.00 m/s, how long does it take the boat to make a complete round trip of 1 100 m upstream followed by a 1 100-m trip downstream?

211 s

A stone is thrown with an initial speed of 11.5 m/s at an angle of 50.0 above the horizontal from the top of a 30.0-m-tall building. Assume air resistance is negligible, and g = 9.8 m/s2. What is the magnitude of the vertical-velocity component of the rock as it hits the ground?

25.8 m/s

A stone is thrown with an initial speed of 11.5 m/s at an angle of 50.0 above the horizontal from the top of a 30.0-m-tall building. Assume air resistance is negligible, and g = 9.8 m/s2. What is the speed of the rock as it hits the ground?

26.8 m/s

Wiley Coyote has missed the elusive road runner once again. This time, he leaves the edge of the cliff at 52.4 m/s horizontal velocity. If the canyon is 140 m deep, how far from his starting point at the edge of the cliff does the coyote land?

280 m

An object, initially moving in the negative x-direction, is subjected to a change in velocity in the positive y-direction. If the resulting velocity vector is drawn from the origin, into which quadrant does this vector point?

2nd

​Suppose a particle is moving along a straight line with a speed v for a time t, then stops for a time t, and then resumes moving along the original direction with speed v for time t. What has been the average speed of the particle for the total time period 3t?

2v/3

A speeding car traveling at a constant velocity of v passes a police car initially at rest beside the roadway. If the police car with constant acceleration of a immediately pursues the speeding car, how long is it before the police car is directly behind the speeding car?

2v/a

A bird, accelerating from rest at a constant rate, experiences a displacement of 25 m in 15 s. What is the final velocity after 15 s?​

3.3 m/s

A rock is thrown straight up with an initial velocity of 17.6 m/s. What time interval elapses between the rock's being thrown and its return to the original launch point? (Acceleration due to gravity is 9.80 m/s2.)

3.60 s

Starting from rest, a car accelerates down a straight road with constant acceleration a for a time t, then the direction of the acceleration is reversed, (i.e., it is −a), and the car comes to a stop in an additional time t, the time for the whole trip being 2t. At what time, or times, is the average velocity of the car for the trip equal to its instantaneous velocity during the trip?

This occurs at 2 times, 0.5t and 1.5t.

In the case of constant acceleration, the average velocity equals the instantaneous velocity:

half-way through the time interval.

A projectile is launched at an angle less than 30° and at speed v. Which will increase the projectile's range more, ignoring atmospheric drag?

increasing the speed of launch by 50%

A plane is moving due north, directly towards its destination. Its airspeed is 220 mph. A constant breeze is blowing from west to east at 50 mph. How long will it take for the plane to travel 220 miles north?​

more than one hour

A v vs. t graph is drawn for a ball moving in one direction. The graph starts at the origin and at t = 5 s the acceleration of the ball is zero. We know that at t = 5 s,

the velocity of the ball is not changing.

A projectile is thrown horizontally at 11.5 m/s. The projectile hits the ground 0.570 s later. What is the angle of impact the projectile makes with the horizontal ground?

-25.9°

A mouse starts out in a corner of a room, and runs across the floor according to the following displacements: d1: 1.2 m + 0.4 m d2: 0.2 m - 0.8 m What is the magnitude of the total displacement of the mouse's position?

1.5 m

A baseball is released at rest from the top of the Washington Monument. It hits the ground after falling for 5.85 s. What was the height from which the ball was dropped? (g = 9.80 m/s2 and assume air resistance is negligible)​

1.68 × 102 m

A 50.0-g ball traveling at 22.0 m/s is bounced off a brick wall and rebounds at 21.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 2.50 ms, what is the average acceleration of the ball during this time interval?

1.72E+4 m/s2

At the top of a cliff 100 m high, Raoul throws a rock upward with velocity 15.0 m/s. How much later should he drop a second rock from rest so both rocks arrive simultaneously at the bottom of the cliff?​

1.78 s

A projectile is fired directly upwards at 49.4 m/s. A second projectile is dropped from rest at some higher elevation at the instant the first projectile is fired and passes the first projectile 3.00 s later. From the frame of reference of the first projectile, what is the velocity of the second projectile as it passes by?

49.4 m/s, downward

A baseball leaves the bat with a speed of 47 m/s and an angle of 45° above the horizontal. A 5.0-m-high fence is located at a horizontal distance of 137 m from the point where the ball is struck. Assuming the ball leaves the bat 1.0 m above ground level, by how much does the ball clear the fence?

49.7 m

A jet airliner moving at 470 mph due east moves into a region where the wind is blowing at 110 mph in a direction 30.0° north of east. What is the new velocity and direction of the aircraft?

568 mph, 5.56° N of E

A plane is moving due north, directly towards its destination. Its airspeed is 210 mph. A constant breeze is blowing from west to east at 25.0 mph. In which direction is the plane pointed?

6.79° W of N

A drag racer starts from rest and accelerates at 8.0 m/s2 for the entire distance of 300 m. What is the velocity of the race car at the end of the run?

69 m/s

A stone is thrown with an initial speed of 11.5 m/s at an angle of 50.0 above the horizontal from the top of a 30.0-m-tall building. Assume air resistance is negligible, and g = 9.8 m/s2. What is the magnitude of the horizontal-velocity component of the rock as it hits the ground?

7.39 m/s

A rifle is aimed horizontally toward the center of a target 120 m away. If the bullet strikes 11.2 cm below the center, what was the velocity of the bullet? (Ignore air friction.)

790 m/s

Two projectiles are launched at 100 m/s, the angle of elevation for the first being 30° and for the second 60°. Which of the following statements is false?

All of the above statements are true.

Two objects of different mass are released simultaneously from the top of a 20-m tower and fall to the ground. If air resistance is negligible, which statement best applies?

Both objects hit the ground together.

A ball of relatively low density is thrown upwards. Because of air resistance the acceleration while traveling upwards is −10.8 m/s2. On its trip downward the resistance is in the opposite direction, and the resulting acceleration is −8.8 m/s2. When the ball reaches the level from which it was thrown, how does its speed compare to that with which it was thrown?

It is less than the original speed upward.

An object is dropped from a height. Once it is moving, which of the following statements is true, at least at one point?

Its velocity is never equal to its acceleration.

A hiker walks 200 m west and then walks 100 m north. In what direction is her resulting displacement?

None of the answers is correct.

A car is moving in the positive direction along a straight highway and accelerates at a constant rate while going from point A to point B. If the acceleration is positive, increasing the speed of the car, when does the position where the average speed equals the instantaneous speed occur during the time interval from A to B? Assume the time interval is T.

T/2 from the start of the interval

On a velocity-time graph for a particle, suppose the plot starts at some positive velocity and then follows a straight line to zero at a later time. Which of the following must be true about a position vs. time graph for this same time interval?

The curve will rise steeply at first and as time goes on will level out approaching its highest position value at the later time.

Two baseballs are released at the same time. One is dropped from rest and the other is given an initial horizontal velocity. Which of the following is not true? Ignore atmospheric drag.

The horizontal component of velocity increases at a greater rate than the vertical component of velocity for both while they are both in the air.

A projectile is launched at an angle θ above the horizontal. Three seconds later the projectile is moving the same angle θ below the horizontal. Which of the following (actual values with units, not just algebraic symbols) can be found from the information given?

the initial vertical component of the projectile's velocity

Starting from rest, a car accelerates down a straight road with constant acceleration a1 for a time t1, then the acceleration is changed to a different constant value a2 for an additional time t2. The total elapsed time is t1 + t2. Can the equations of kinematics be used to find the total distance traveled?

Yes, break the problem up into 2 problems, one with the conditions for the first time interval and the other with the conditions for the second time interval, noting that for the second time interval the initial velocity is that from the end of the first time interval. When done, add the distances from each of the time intervals.

A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher. At what point is the magnitude of the acceleration at a minimum? (air resistance is negligible)

acceleration is constant during entire trajectory

Which formula is dimensionally consistent with an expression yielding a value for velocity? (a is acceleration, x is distance, and t is time)

at

A baseball catcher throws a ball vertically upward and catches it in the same spot when it returns to his mitt. At what point in the ball's path does it experience zero velocity and non-zero acceleration at the same time?

at the top of its trajectory

On a position-versus-time graph, the slope of the straight line joining two points on the plotted curve that are separated in time by the interval Δt, is which of the following quantities?

average velocity

In a two-dimensional Cartesian coordinate system the x-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and x-axis?

cosine

In a two-dimensional Cartesian system, the x-component of a vector is known, and the angle between vector and x-axis is known. Which operation is used to calculate the magnitude of the vector? (taken with respect to the x-component)

dividing by cosine

If the displacement of an object is given in SI units by Δx = −3t + 4t 2, at t = 2 s its velocity and acceleration are, respectively:

positive, positive

The value of an object's acceleration may be characterized in equivalent words by which of the following?

rate of change of velocity

Changing the positive direction in a reference frame to the opposite direction does not change the sign of which of the following quantities?

speed

A strobe photograph shows equally-spaced images of a car moving along a straight road. If the time intervals between images is constant, which of the following cannot be positive?

the acceleration of the car

If a is acceleration, v is velocity, x is position, and t is time, then which equation is not dimensionally correct?

v = a/t

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 28.3 m/s at an initial angle of 30.0° with respect to the horizontal. If it is in its trajectory for a total of 4.00 s before being caught by the third baseman at an equal shoulder-height level, what is the ball's net vertical displacement during its 4.00-s trajectory?​

zero