Question 1

The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by ​  and  m/s.
​
The plane is most likely

Accepted Answer

A) just touching down. 
B) in level flight in the air. 
C) ascending. 
D) descending. 
E) taking off.

Question 2

The position of an object is given by  where t is in seconds. At t = 2.0 s, what is the magnitude of the particle's acceleration?

Accepted Answer

A) 0 m/s2 
B) 2.0 m/s2 
C) 17 m/s2 
D) 36 m/s2 
E) 72 m/s2

Question 3

Given the equations below, which description best fits the physical situation?

Accepted Answer

A) A projectile's displacement two seconds after being fired downward with a speed of 30.0 m/s. 
B) A projectile's displacement two seconds after being fired downward with a speed of 40.0 m/s. 
C) A projectile's displacement two seconds after being fired downward with a speed of 50.0 m/s. 
D) A projectile's displacement two seconds after being fired downward with a speed of 60.0 m/s. 
E) A projectile's displacement two seconds after being fired downward with a speed of 80.0 m/s.

Question 4

Wiley Coyote has missed the elusive roadrunner once again. This time, he leaves the edge of the cliff at 50.0 m/s horizontal velocity. If the canyon is 100 m deep, how far from the edge of the cliff does the coyote land?

Accepted Answer

The answer of Wiley Coyote has missed the elusive roadrunner...

Question 5

In a location where the train tracks run parallel to a road, a high speed train traveling at 60 m/s passes a car traveling at 30 m/s. How long does it take for the train to be 180 m ahead of the car?

Accepted Answer

A) 2.0 s 
B) 3.0 s 
C) 6.0 s 
D) 9.0 s 
E) 18.0 s

Question 6

In a location where the train tracks run parallel to a road, a high speed train traveling at 60 m/s passes a car traveling at 30 m/s in the opposite direction. How long does it take for the train to be 180 m away from the car?

Accepted Answer

A) 2.0 s 
B) 3.0 s 
C) 6.0 s 
D) 9.0 s 
E) 18.0 s

Question 7

A projectile is thrown from the top of a building with an initial velocity of 30 m/s in the horizontal direction. If the top of the building is 30 m above the ground, how fast will the projectile be moving just before it strikes the ground?

Accepted Answer

A) 35 m/s 
B) 39 m/s 
C) 31 m/s 
D) 43 m/s 
E) 54 m/s

Question 8

A car travels counterclockwise around a flat circle of radius 0.25 km at a constant speed of 20 m/s. When the car is at point A as shown in the figure, what is the car's acceleration?

Accepted Answer

A) 1.6 m/s2, south 
B) Zero 
C) 1.6 m/s2, east 
D) 1.6 m/s2, north 
E) 1.6 m/s2, west

Question 9

A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 24 m/s west, and the acceleration of the car has components of 2.4 m/s2 east and 1.8 m/s2 south. What is the radius of the circle?

Accepted Answer

A) 0.24 km 
B) 0.19 km 
C) 0.32 km 
D) 0.14 km 
E) 0.27 km

Question 10

An airplane flies horizontally with a speed of 300 m/s at an altitude of 400 m. Assume that the ground is level. At what horizontal distance from a target must the pilot release a bomb so as to hit the target?

Accepted Answer

A) 3.0 km 
B) 2.4 km 
C) 3.3 km 
D) 2.7 km 
E) 1.7 km

Question 11

A block is supported on a compressed spring, which projects the block straight up in the air at velocity  . The spring and ledge it sits on then retract. You can win a prize by hitting the block with a ball. When should you throw the ball and in what direction to be sure the ball hits the block? (Assume the ball can reach the block before the block reaches the ground and that the ball is thrown from a height equal to the release position of the block.)

Accepted Answer

A) At the instant when the block leaves the spring, directed at the block 
B) At the instant when the block leaves the spring, directed at the spring 
C) At the instant when the block is at the highest point, directed at the block 
D) At the instant when the block is at the highest point, directed at the spring 
E) When the block is back at the spring's original position, directed at that position

Question 12

A rock is thrown from the edge of the top of a 100-ft tall building at some unknown angle above the horizontal. The rock strikes the ground a horizontal distance of 160 ft from the base of the building 5.0 s after being thrown. Assume that the ground is level and that the side of the building is vertical. Determine the speed with which the rock was thrown.

Accepted Answer

A) 72 ft/s 
B) 77 ft/s 
C) 68 ft/s 
D) 82 ft/s 
E) 87 ft/s

Question 13

While the gondola is rising at a speed of 5.0 m/s, a passenger in a balloon-supported gondola throws a small ball up at a speed of 2.0 m/s relative to his body. A person who measures the ball's velocity at the instant of release will find that the ball's velocity relative to the ground at that instant is

Accepted Answer

A) 2.0 m/s, up. 
B) 2.8 m/s, down. 
C) 3.0 m/s, up. 
D) 5.0 m/s, up. 
E) 7.0 m/s, up.

Question 14

The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by ​  and  m/s.
​
The plane is most likely

Accepted Answer

A) just touching down. 
B) in level flight in the air. 
C) ascending. 
D) descending. 
E) taking off.

Question 15

A car is driven 1200 m north at 20.0 m/s and then driven 1600 m east at 25.0 m/s. What is the magnitude of the average velocity for this trip?

Accepted Answer

A) 16.1 m/s 
B) 22.6 m/s 
C) 31.3 m/s 
D) 11.3 m/s 
E) 62.2 m/s

Question 16

Car A leaves point O at t = 0 and travels a quarter circle counterclockwise at 30.0 m/s to point P. Car B will leave point O and travel to point P at the same speed but in a straight line. The radius of the circle is 100 m. At what time should car B leave point O in order to arrive at point P at the same time as car A?

Accepted Answer

A) At t = 0. 
B) At t = 0.52 s. 
C) At t = 4.71 s. 
D) At t = 4.98 s. 
E) At t = 5.24 s.

Question 17

A 0.14-km wide river flows with a uniform speed of 4.0 m/s toward the east. It takes 20 s for a boat to cross the river to a point directly north of its departure point on the south bank. What is the speed of the boat relative to the water?

Accepted Answer

A) 5.7 m/s 
B) 8.5 m/s 
C) 8.1 m/s 
D) 7.0 m/s 
E) 6.4 m/s

Question 18

Two cars are traveling around identical circular racetracks. Car A travels at a constant speed of 20 m/s. Car B starts at rest and speeds up with constant tangential acceleration until its speed is 40 m/s. When car B has the same (tangential) velocity as car A, it is always true that:

Accepted Answer

A) it is passing car A. 
B) it has the same linear (tangential) acceleration as car A. 
C) it has the same centripetal acceleration as car A. 
D) it has the same total acceleration as car A. 
E) it has traveled farther than car A since starting.

Question 19

A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 20 m/s north, and the total acceleration of the car is 2.5 m/s2 37° south of west. Which of the following is correct?

Accepted Answer

A) R = 0.40 km, and the car's speed is decreasing. 
B) R = 0.20 km, and the car's speed is decreasing. 
C) R = 0.20 km, and the car's speed is increasing. 
D) R = 0.16 km, and the car's speed is increasing. 
E) R = 0.16 km, and the car's speed is decreasing.

Exam 4: Two- and Three-Dimensional Motion

The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by and m/s. The plane is most likely

The position of an object is given by where t is in seconds. At t = 2.0 s, what is the magnitude of the particle's acceleration?

Given the equations below, which description best fits the physical situation?

Wiley Coyote has missed the elusive roadrunner once again. This time, he leaves the edge of the cliff at 50.0 m/s horizontal velocity. If the canyon is 100 m deep, how far from the edge of the cliff does the coyote land?

In a location where the train tracks run parallel to a road, a high speed train traveling at 60 m/s passes a car traveling at 30 m/s. How long does it take for the train to be 180 m ahead of the car?

In a location where the train tracks run parallel to a road, a high speed train traveling at 60 m/s passes a car traveling at 30 m/s in the opposite direction. How long does it take for the train to be 180 m away from the car?

A projectile is thrown from the top of a building with an initial velocity of 30 m/s in the horizontal direction. If the top of the building is 30 m above the ground, how fast will the projectile be moving just before it strikes the ground?

A car travels counterclockwise around a flat circle of radius 0.25 km at a constant speed of 20 m/s. When the car is at point A as shown in the figure, what is the car's acceleration?

A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 24 m/s west, and the acceleration of the car has components of 2.4 m/s² east and 1.8 m/s² south. What is the radius of the circle?

An airplane flies horizontally with a speed of 300 m/s at an altitude of 400 m. Assume that the ground is level. At what horizontal distance from a target must the pilot release a bomb so as to hit the target?

The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by and m/s. The plane is most likely

A car is driven 1200 m north at 20.0 m/s and then driven 1600 m east at 25.0 m/s. What is the magnitude of the average velocity for this trip?

A 0.14-km wide river flows with a uniform speed of 4.0 m/s toward the east. It takes 20 s for a boat to cross the river to a point directly north of its departure point on the south bank. What is the speed of the boat relative to the water?

Two cars are traveling around identical circular racetracks. Car A travels at a constant speed of 20 m/s. Car B starts at rest and speeds up with constant tangential acceleration until its speed is 40 m/s. When car B has the same (tangential) velocity as car A, it is always true that:

A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 20 m/s north, and the total acceleration of the car is 2.5 m/s² 37° south of west. Which of the following is correct?

Exam 4: Two- and Three-Dimensional Motion

The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by ​ and m/s. ​ The plane is most likely

The position of an object is given by where t is in seconds. At t = 2.0 s, what is the magnitude of the particle's acceleration?

Given the equations below, which description best fits the physical situation?

Wiley Coyote has missed the elusive roadrunner once again. This time, he leaves the edge of the cliff at 50.0 m/s horizontal velocity. If the canyon is 100 m deep, how far from the edge of the cliff does the coyote land?

In a location where the train tracks run parallel to a road, a high speed train traveling at 60 m/s passes a car traveling at 30 m/s. How long does it take for the train to be 180 m ahead of the car?

In a location where the train tracks run parallel to a road, a high speed train traveling at 60 m/s passes a car traveling at 30 m/s in the opposite direction. How long does it take for the train to be 180 m away from the car?

A projectile is thrown from the top of a building with an initial velocity of 30 m/s in the horizontal direction. If the top of the building is 30 m above the ground, how fast will the projectile be moving just before it strikes the ground?

A car travels counterclockwise around a flat circle of radius 0.25 km at a constant speed of 20 m/s. When the car is at point A as shown in the figure, what is the car's acceleration?

A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 24 m/s west, and the acceleration of the car has components of 2.4 m/s2 east and 1.8 m/s2 south. What is the radius of the circle?

An airplane flies horizontally with a speed of 300 m/s at an altitude of 400 m. Assume that the ground is level. At what horizontal distance from a target must the pilot release a bomb so as to hit the target?

The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by ​ and m/s. ​ The plane is most likely

A car is driven 1200 m north at 20.0 m/s and then driven 1600 m east at 25.0 m/s. What is the magnitude of the average velocity for this trip?

A 0.14-km wide river flows with a uniform speed of 4.0 m/s toward the east. It takes 20 s for a boat to cross the river to a point directly north of its departure point on the south bank. What is the speed of the boat relative to the water?

Two cars are traveling around identical circular racetracks. Car A travels at a constant speed of 20 m/s. Car B starts at rest and speeds up with constant tangential acceleration until its speed is 40 m/s. When car B has the same (tangential) velocity as car A, it is always true that:

A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 20 m/s north, and the total acceleration of the car is 2.5 m/s2 37° south of west. Which of the following is correct?

The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by and m/s. The plane is most likely

A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 24 m/s west, and the acceleration of the car has components of 2.4 m/s² east and 1.8 m/s² south. What is the radius of the circle?

The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by and m/s. The plane is most likely

A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 20 m/s north, and the total acceleration of the car is 2.5 m/s² 37° south of west. Which of the following is correct?