Question 1

The velocity of an object with respect to reference frame A is equal to

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Question 2

If reference frame A is in motion with respect to reference frame B, the velocity of an object with respect to frame A

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Question 3

A boat is trying to cross a river that flows due north with a strong current. The boat starts at point A on the west bank and will reach the east bank directly across from the starting point. The boat should head

Accepted Answer

To counteract the northward flow of the river and reach a point directly across on the east bank, the boat should aim southeast. This direction allows the boat to make headway against the current while also moving across the river.

Question 4

A boy is shooting marbles on a flatcar that is itself in uniform motion on a straight, horizontal track. The boy can shoot marbles at a speed of 30 m/s with respect to the flatcar. The speed of the flatcar with respect to the train track rails is 40 m/s. The maximum possible horizontal speed of a marble with respect to the rails is

Accepted Answer

The maximum possible horizontal speed of a marble with respect to the rails is when the marble is shot in the same direction as the flatcar's motion. In this case, the speeds add up: 30 m/s (marble with respect to flatcar) + 40 m/s (flatcar with respect to rails) = 70 m/s.

Question 5

A car travels due east with a speed of 40.0 km/h. Raindrops are falling at a constant speed of 30.0 km/h vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of

Accepted Answer

The angle of the rain traces with the vertical can be found using the tangent of the angle, which is the ratio of the horizontal speed of the car to the vertical speed of the rain: tan(θ) = 40/30. Solving for θ gives approximately 53.0° with the vertical.

Question 6

An airplane having a speed relative to the air of 250 km/h needs to land in a city north of the departure airport when the wind blows toward the east at 40 km/h. The pilot should maintain a heading of

Accepted Answer

To counteract the eastward wind and maintain a northward path, the pilot must head slightly west of north. Using vector addition and trigonometry, the angle is approximately 10.1° west of north.

Question 7

A boat travels at a constant speed with respect to still water. Now suppose the water is moving with respect to the bank at a speed almost as large as the speed of the boat with respect to still water. Compare the time taken for a round trip of constant distance (with respect to the bank) in the boat under two scenarios: downstream, then upstream or cross-stream, then back. The "down-up" time is

Accepted Answer

When traveling downstream and then upstream, the effective speed of the boat is reduced due to the current, increasing the round trip time compared to traveling across the stream and back, where the current has no effect on the round trip time.

Question 8

A boat travels at a constant speed with respect to still water. The water is moving with respect to the bank at a speed almost as large as the speed of the boat with respect to still water. Assume a round trip of constant distance (with respect to the bank) in the boat under two scenarios: downstream, then upstream or cross-stream, then back. All of the following statements are correct except

Accepted Answer

The cross-stream time is actually dependent on the stream speed compared to the boat speed, as the boat has to compensate for the stream's movement to maintain its course, affecting the time taken for the cross-stream journey.

Question 9

A school bus travels east at 40 km/h. Alex, sitting on the left side of the bus, throws a tennis ball at 30 km/h to Brendan, who is seated on the right side of the bus, directly across from Alex. The velocity of the ball as seen by Kyle, standing next to the road, is

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Question 10

A school bus travels east at 10 km/h. Alex, sitting in the back of the bus throws a tennis ball at Brendan. Kyle, standing next to the road, observes the ball moving at 60 km/h south. The direction of the velocity of the ball with respect to the bus is

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Quiz 4: Motion in Two and Three Dimensions