APP1 - 1.4 APC

Water in a river flows uniformly to the east with a speed of 5 m/s relative to the shore. A boat is traveling to the west at 10 m/s relative to the water. A passenger on the boat is walking at 5 m/s to the east, toward the back of the boat. Which of the following statements about the passenger’s velocity is correct and gives the correct reason?

• The passenger is moving at 20 m/s relative to the shore because the boat is moving at 5 m/s relative to the shore and the passenger is moving at 15 m/s relative to the water.

• The passenger is moving at 20 m/s relative to the shore because the sum of all of the velocities (10 m/s, 5 m/s, and 5 m/s) is 20 m/s.

• The passenger is stationary relative to the shore because the boat is moving at 5 m/s relative to the shore and the passenger is moving at 5 m/s relative to the boat in the opposite direction.

• The passenger is stationary relative to the shore because the boat is moving at 15 m/s relative to the water and the passenger is moving at 15 m/s in the opposite direction relative to the water.

A student is riding on a bus that is traveling east at a constant speed. The student walks toward the front of the bus. A stationary observer outside the bus standing on the road claims that the student is moving faster than the bus. Is the claim correct? Why or why not?

• No, because the student is included in the same frame of reference as the bus so the student and bus must be traveling at the same speed.

• No, because the student, bus, and observer are all included in Earth’s reference frame so the student and bus must be traveling at the same speed.

• Yes, because according to the stationary observer, the student’s velocity is the velocity of the bus plus the velocity of the student relative to the bus.

• Yes, because according to the stationary observer, the student’s velocity is the difference between the velocity of the bus and the velocity of the student relative to the bus.

A rowboat moving in a lake is accelerating at a constant rate towards the shore. An observer in another boat moving at a constant velocity measures the row boat’s acceleration. A second observer, standing still on the shore, also measures the acceleration of the rowboat. Are the two accelerations measured by the two observers the same? Why or why not?

• No, because the observer on the other boat is in a non-inertial reference frame.

• No, because the observers have different velocities relative to the rowboat.

• Yes, because both observers are in inertial reference frames.

• Yes, because both observers are external to the rowboat’s frame of reference and will therefore measure zero acceleration.

Three vehicles pass each other traveling on a three-lane roadway. Vehicle A is moving west with speed vA relative to the road; Vehicle B is moving east with speed vB relative to the road; and Vehicle C is moving east with speed vC relative to the road. Assume east is the positive direction. What is the velocity of Vehicle B relative to observers in Vehicle A and in Vehicle C?

• vB + vA, vB + vC

• vB + vA, vB - vC

• vB - vA, vB + vC

• vB - vA, vB - vC

• 7 m/s

• 6 m/s

• 5 m/s

• 3 m/s

A cart equipped with a launcher launches a dart horizontally, as shown. The dart is always given the same horizontal velocity v_dart relative to the cart. In Trial 1, the cart is at rest at Point P a distance D from a target and launches the dart toward the target. The dart takes a time t_1 to reach the target. In Trial 2, the cart is moving toward the target with constant speed v_cart and launches the dart at the instant the cart is at Point P. The dart takes a time t_2 to reach the target. The cart has a negligible change in speed during the launch. Which of the following is a correct expression for the cart’s speed v_cart?

• D / (t_1 + t_2)

• D / (t_1 - t_2)

• D / t_1 + D / t_2

• D / t_2 - D / t_1

A duck flies past a truck that is at rest. The duck takes 2.1 seconds to fly at constant speed v_d from the back of the truck to the front. Later, the truck travels along a flat, straight roadway with a constant speed (3/4)v_d. The duck again flies past the truck with constant speed v_d, flying in the same direction that the truck is moving. How long does it take the duck to fly from the back of the truck to the front in this case?

• 1.2 seconds

• 1.6 seconds

• 2.8 seconds

• 8.4 seconds

A train is moving to the east at 25 m/s relative to the ground. A passenger at the back of the train throws a ball to the west with an initial speed of 15 m/s relative to the train. What is the initial velocity of the ball relative to the ground?

• 10 m/s to the east

• 10 m/s to the west

• 40 m/s to the east

• 40 m/s to the west