Relative motion Knowledge-Based Practice

Questions

1. 1.

   A boat travels at a constant speed of 10 m/s relative to the water across a straight river with a current flowing at 6.0 m/s. If the boat is steered upstream so that its path relative to the ground is directly perpendicular to the riverbanks, what is the speed of the boat relative to the ground?

   • A) 4.0 m/s
   • B) 8.0 m/s
   • C) 11.7 m/s
   • D) 16.0 m/s
2. 2.

   A car travels along a straight road at a constant speed of 30 m/s. The instant it passes a stationary motorcycle, the motorcycle accelerates from rest in the same direction at a constant rate of 3.0 m/s². What is the maximum separation distance between the two vehicles?

   • A) 75 m
   • B) 100 m
   • C) 150 m
   • D) 300 m
3. 3.

   A passenger takes 60 s to travel the length of an airport moving walkway when standing still on it, and 30 s when walking along it while the walkway is stationary. How much time does it take the passenger to travel the same distance when walking along the moving walkway in the direction of its motion?

   • A) 15 s
   • B) 20 s
   • C) 45 s
   • D) 90 s
4. 4.

   Two particles, A and B, move in a plane with velocities $\vec{v}_A = (7\hat{i} + 6\hat{j})\text{ m/s}$ and $\vec{v}_B = (3\hat{i} + 3\hat{j})\text{ m/s}$ relative to the ground. What is the magnitude of the velocity of particle A relative to particle B?

   • A) 1 m/s
   • B) 7 m/s
   • C) 5 m/s
   • D) 25 m/s
5. 5.

   A swimmer travels 120 m downstream along a straight river in 30 s and takes 60 s to swim the same distance upstream. What is the speed of the river current?

   • A) 0.5 m/s
   • B) 1.0 m/s
   • C) 2.0 m/s
   • D) 3.0 m/s
6. 6.

   A 150 m long train travels east at a constant speed of 20 m/s, while a 200 m long train travels west on an adjacent parallel track at a constant speed of 15 m/s. How much time elapses from the instant the front ends of the trains meet until their rear ends completely clear each other?

   • A) 5 s
   • B) 10 s
   • C) 20 s
   • D) 70 s
7. 7.

   A boat crosses a 300 m wide river by steering perpendicular to the riverbanks at a constant speed of 5.0 m/s relative to the water. If the river current flows parallel to the banks at a uniform speed of 3.0 m/s, how far downstream from the point directly opposite its starting point does the boat reach the opposite bank?

   • A) 100 m
   • B) 120 m
   • C) 180 m
   • D) 300 m
8. 8.

   Two runners, X and Y, move in the same direction along a straight track at constant speeds of 6 m/s and 4 m/s relative to the ground, respectively. If Runner X is initially 60 m behind Runner Y, how long does it take Runner X to catch up to Runner Y?

   • A) 30 s
   • B) 6 s
   • C) 10 s
   • D) 15 s
9. 9.

   An airplane flies a round trip between two airports separated by a distance of 180 km along an east-west line. If the airplane maintains a cruising speed of 90 km/h relative to the air and a steady wind blows east at 30 km/h along this line, what is the total flight time for the round trip?

   • A) 3.5 h
   • B) 4.0 h
   • C) 4.5 h
   • D) 5.0 h
10. 10.

    An airplane needs to travel due north relative to the ground while a steady wind blows toward the east. In which direction relative to the air must the airplane be steered to maintain this ground track?

    • A) East of north
    • B) West of north
    • C) Due north
    • D) West of south
11. 11.

    A car travels along a straight, level road at a constant velocity. An observer inside the car and a stationary observer on the sidewalk both track the motion of a ball tossed inside the car. Which kinematic quantity of the ball is identical in both observers' frames of reference?

    • A) Position
    • B) Velocity
    • C) Displacement
    • D) Acceleration
12. 12.

    A railcar travels horizontally along a straight track at a constant velocity, and an object is projected vertically upward from the railcar relative to the car. Neglecting air resistance, what is the shape of the object's trajectory as observed by a stationary observer standing on the ground?

    • A) A parabola
    • B) A vertical straight line
    • C) A horizontal straight line
    • D) A circular arc
13. 13.

    A boat moves with a constant speed relative to the water across a straight river that has a uniform current flowing parallel to its banks. To reach the opposite bank in the shortest possible time, in which direction must the boat head relative to the water?

    • A) Directly perpendicular to the riverbanks
    • B) Angled upstream so that the boat's resultant velocity relative to the bank is perpendicular to the flow
    • C) Angled downstream at $45^\circ$ to the current to maximize total speed relative to the bank
    • D) Directly downstream in the direction of the river current
14. 14.

    Rain falls vertically downward at a constant speed of 5.0 m/s relative to the ground. If a person walks horizontally at 5.0 m/s relative to the ground, at what angle to the vertical do the raindrops appear to fall from the person's frame of reference?

    • A) 0°
    • B) 30°
    • C) 45°
    • D) 60°
15. 15.

    Two stones are dropped from rest from the same height, with the second stone released 1.0 s after the first. Neglecting air resistance, how does the velocity of the first stone relative to the second stone change as they both fall?

    • A) It remains constant.
    • B) It increases at a constant rate.
    • C) It decreases at a constant rate.
    • D) It becomes zero after both are in motion.
16. 16.

    A drone flies due north at a constant speed of 12 m/s relative to the ground, while a second drone flies due west at a constant speed of 5 m/s relative to the ground. What is the magnitude of the velocity of the first drone relative to the second drone?

    • A) 13 m/s
    • B) 17 m/s
    • C) 7 m/s
    • D) 11 m/s
17. 17.

    Two cyclists, A and B, travel due north along a straight path at constant speeds of 8 m/s and 12 m/s relative to the ground, respectively. What is the velocity of Cyclist A relative to Cyclist B?

    • A) 20 m/s due south
    • B) 4 m/s due north
    • C) 4 m/s due south
    • D) 20 m/s due north
18. 18.

    A boat heads due east across a river at 4.0 m/s relative to the water, while the river current flows due south at 3.0 m/s relative to the riverbank. What is the magnitude of the velocity of the boat relative to the riverbank?

    • A) 1.0 m/s
    • B) 3.5 m/s
    • C) 7.0 m/s
    • D) 5.0 m/s
19. 19.

    A train travels north at a constant speed of 20 m/s relative to the ground. What is the velocity of a passenger relative to the ground if they walk toward the back of the train at 2 m/s relative to the train?

    • A) 22 m/s to the north
    • B) 18 m/s to the north
    • C) 18 m/s to the south
    • D) 22 m/s to the south
20. 20.

    Car A travels along a straight road to the east at a constant speed of 25 m/s, while Car B travels along an adjacent parallel lane to the west at a constant speed of 15 m/s. What is the velocity of Car A with respect to Car B?

    • A) 10 m/s east
    • B) 10 m/s west
    • C) 40 m/s west
    • D) 40 m/s east

Answers and step-by-step solutions appear after you finish the test.