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Two cooks standing side by side in a restaurant pull their beaters out of the dough at the same instant. A glob of dough flies off each beater. Each glob lands on the top of a tin the same horizontal distance away and at its initial height. However, one lands later than the other. The explanation is that they left the beaters at angles θ1 and θ2 such that:


A) θ2 = −θ1.
B) θ1 + θ2 =
Two cooks standing side by side in a restaurant pull their beaters out of the dough at the same instant. A glob of dough flies off each beater. Each glob lands on the top of a tin the same horizontal distance away and at its initial height. However, one lands later than the other. The explanation is that they left the beaters at angles θ<sub>1</sub> and θ<sub>2</sub> such that: A) θ<sub>2</sub> = −θ<sub>1</sub>. B) θ<sub>1</sub> + θ<sub>2</sub> = . C) θ<sub>1</sub> + θ<sub>2</sub> = . D) θ<sub>1</sub> + θ<sub>2</sub> = π. E) θ<sub>1</sub> − θ<sub>2</sub> = π. .
C) θ1 + θ2 =
Two cooks standing side by side in a restaurant pull their beaters out of the dough at the same instant. A glob of dough flies off each beater. Each glob lands on the top of a tin the same horizontal distance away and at its initial height. However, one lands later than the other. The explanation is that they left the beaters at angles θ<sub>1</sub> and θ<sub>2</sub> such that: A) θ<sub>2</sub> = −θ<sub>1</sub>. B) θ<sub>1</sub> + θ<sub>2</sub> = . C) θ<sub>1</sub> + θ<sub>2</sub> = . D) θ<sub>1</sub> + θ<sub>2</sub> = π. E) θ<sub>1</sub> − θ<sub>2</sub> = π. .
D) θ1 + θ2 = π.
E) θ1 − θ2 = π.

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While the gondola is rising at a speed of 2.0 m/s, a passenger in a balloon-supported gondola throws a small ball down at a speed of 5.0 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


A) 2.0 m/s, up.
B) 3.0 m/s, down.
C) 3.0 m/s, up.
D) 5.0 m/s, down.
E) 12.8 m/s, down.

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A particle leaves the origin with a velocity of 7.2 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (3.0 A particle leaves the origin with a velocity of 7.2 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (3.0 − 2.0 ) m/s<sup>2</sup>. At the instant the particle moves back across the x axis (y = 0) , what is the value of its x coordinate? A) 65 m B) 91 m C) 54 m D) 78 m E) 86 m − 2.0 A particle leaves the origin with a velocity of 7.2 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (3.0 − 2.0 ) m/s<sup>2</sup>. At the instant the particle moves back across the x axis (y = 0) , what is the value of its x coordinate? A) 65 m B) 91 m C) 54 m D) 78 m E) 86 m ) m/s2. At the instant the particle moves back across the x axis (y = 0) , what is the value of its x coordinate?


A) 65 m
B) 91 m
C) 54 m
D) 78 m
E) 86 m

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A motorcycle daredevil wants to ride up a 50.0 m ramp set at a 30.0° incline to the ground. It will launch him in the air and he wants to come down so he just misses the last of a number of 1.00 m diameter barrels. If the speed at the instant when he leaves the ramp is 60.0 m/s, how many barrels can be used?


A) 79
B) 318
C) 332
D) 355
E) 402

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Exhibit 4-1 While her kid brother is on a wooden horse at the edge of a merry-go-round, Sheila rides her bicycle parallel to its edge. The wooden horses have a tangential speed of 6 m/s. Sheila rides at 4 m/s. The radius of the merry-go-round is 8 m. Use this exhibit to answer the following question(s) . -Refer to Exhibit 4-1. At what time intervals does Sheila encounter her brother, if she rides opposite to the direction of rotation of the merry-go-round?


A) 5.03 s
B) 8.37 s
C) 12.6 s
D) 25.1 s
E) 50.2 s

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A block is supported on a compressed spring, which projects the block straight up in the air at velocity 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.) 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. . 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.)


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.

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The pilot of an aircraft flies due north relative to the ground in a wind blowing 40 km/h toward the east. If his speed relative to the ground is 80 km/h, what is the speed of his airplane relative to the air?


A) 89 km/h
B) 85 km/h
C) 81 km/h
D) 76 km/h
E) 72 km/h

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An object moving at a constant speed requires 6.0 s to go once around a circle with a diameter of 4.0 m. What is the magnitude of the instantaneous acceleration of the particle during this time?


A) 2.2 m/s2
B) 2.7 m/s2
C) 3.3 m/s2
D) 3.8 m/s2
E) 4.4 m/s2

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Exhibit 4-1 While her kid brother is on a wooden horse at the edge of a merry-go-round, Sheila rides her bicycle parallel to its edge. The wooden horses have a tangential speed of 6 m/s. Sheila rides at 4 m/s. The radius of the merry-go-round is 8 m. Use this exhibit to answer the following question(s) . -Refer to Exhibit 4-1. At what time intervals does Sheila encounter her brother, if she rides in the direction of rotation of the merry-go-round?


A) 5.03 s
B) 8.37 s
C) 12.6 s
D) 25.1 s
E) 50.2 s

Correct Answer

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A particle moves in the xy plane in a circle centered on the origin. At a certain instant the velocity and acceleration of the particle are 6.0 A particle moves in the xy plane in a circle centered on the origin. At a certain instant the velocity and acceleration of the particle are 6.0 m/s and (3.0 + 4.0 ) m/s<sup>2</sup>. What are the x and y coordinates of the particle at this moment? A) x = 0, y = −9.0 m B) x = 0, y = +7.2 m C) x = 0, y = +9.0 m D) x = 0, y = −7.2 m E) x = 6.0 m, y = −9.0 m m/s and (3.0 A particle moves in the xy plane in a circle centered on the origin. At a certain instant the velocity and acceleration of the particle are 6.0 m/s and (3.0 + 4.0 ) m/s<sup>2</sup>. What are the x and y coordinates of the particle at this moment? A) x = 0, y = −9.0 m B) x = 0, y = +7.2 m C) x = 0, y = +9.0 m D) x = 0, y = −7.2 m E) x = 6.0 m, y = −9.0 m + 4.0 A particle moves in the xy plane in a circle centered on the origin. At a certain instant the velocity and acceleration of the particle are 6.0 m/s and (3.0 + 4.0 ) m/s<sup>2</sup>. What are the x and y coordinates of the particle at this moment? A) x = 0, y = −9.0 m B) x = 0, y = +7.2 m C) x = 0, y = +9.0 m D) x = 0, y = −7.2 m E) x = 6.0 m, y = −9.0 m ) m/s2. What are the x and y coordinates of the particle at this moment?


A) x = 0, y = −9.0 m
B) x = 0, y = +7.2 m
C) x = 0, y = +9.0 m
D) x = 0, y = −7.2 m
E) x = 6.0 m, y = −9.0 m

Correct Answer

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A particle moves in the xy plane with a constant acceleration given by A particle moves in the xy plane with a constant acceleration given by . At t = 0, its position and velocity are 10 m and , respectively. What is the distance from the origin to the particle at t = 2.0 s? A) 6.4 m B) 10 m C) 8.9 m D) 2.0 m E) 6.2 m . At t = 0, its position and velocity are 10 A particle moves in the xy plane with a constant acceleration given by . At t = 0, its position and velocity are 10 m and , respectively. What is the distance from the origin to the particle at t = 2.0 s? A) 6.4 m B) 10 m C) 8.9 m D) 2.0 m E) 6.2 m m and A particle moves in the xy plane with a constant acceleration given by . At t = 0, its position and velocity are 10 m and , respectively. What is the distance from the origin to the particle at t = 2.0 s? A) 6.4 m B) 10 m C) 8.9 m D) 2.0 m E) 6.2 m , respectively. What is the distance from the origin to the particle at t = 2.0 s?


A) 6.4 m
B) 10 m
C) 8.9 m
D) 2.0 m
E) 6.2 m

Correct Answer

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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 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 . The plane is most likely A) just touching down. B) in level flight in the air. C) ascending. D) descending. E) taking off. and 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 . The plane is most likely A) just touching down. B) in level flight in the air. C) ascending. D) descending. E) taking off. . The plane is most likely


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

Correct Answer

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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 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 . The plane is most likely A) just touching down. B) in level flight in the air. C) ascending. D) descending. E) taking off. and 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 . The plane is most likely A) just touching down. B) in level flight in the air. C) ascending. D) descending. E) taking off. . The plane is most likely


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

Correct Answer

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

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A rock is projected from the edge of the top of a building with an initial velocity of 12.2 m/s at an angle of 53° above the horizontal. The rock strikes the ground a horizontal distance of 25 m from the base of the building. Assume that the ground is level and that the side of the building is vertical. How tall is the building?


A) 25.3 m
B) 29.6 m
C) 27.4 m
D) 23.6 m
E) 18.9 m

Correct Answer

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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?


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

Correct Answer

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


A) 1400 m, northeast
B) 2000 m, 36.9° north of east
C) 2000 m, 53.1° north of east
D) 2800 m, 36.9° east of north
E) 2800 m, 53.1° east of north

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A football is thrown upward at a 30.0° angle to the horizontal. To throw a 40.0-m pass, what must be the initial speed of the ball?

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A river has a steady speed of 0.30 m/s. A student swims downstream a distance of 1.2 km and returns to the starting point. If the student swims with respect to the water at a constant speed and the downstream portion of the swim requires 20 minutes, how much time is required for the entire swim?


A) 50 minutes
B) 80 minutes
C) 90 minutes
D) 70 minutes
E) 60 minutes

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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?

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