While conducting an environmental survey along a straight river, an automated research boat heading upstream passes an unpowered data buoy drifting freely with the current at a fixed sensor station. The boat continues cruising upstream at a constant speed relative to the water for 30 minutes, then instantly turns around and travels downstream at the same speed relative to the water until it overtakes the drifting buoy 3.0 km downstream from the station. Assuming the river current flows at a uniform speed relative to the riverbank, what are the total time elapsed from the initial encounter until the boat overtakes the buoy and the speed of the river current relative to the riverbank?

A) Total time: 60 minutes; speed of current: 3.0 km/h

B) Total time: 45 minutes; speed of current: 4.0 km/h

C) Total time: 30 minutes; speed of current: 6.0 km/h

D) Total time: 90 minutes; speed of current: 2.0 km/h

Two automated test rovers, Rover A and Rover B, travel at constant speeds around a closed circular track with a circumference of 600 m. When the rovers travel in opposite directions, they encounter each other every 30 s. When they travel in the same direction, Rover A overtakes Rover B once every 150 s. What are the constant speeds of Rover A and Rover B relative to the track?

A) Rover A: $16\text{ m/s}$; Rover B: $4\text{ m/s}$

B) Rover A: $14\text{ m/s}$; Rover B: $6\text{ m/s}$

C) Rover A: $10\text{ m/s}$; Rover B: $6\text{ m/s}$

D) Rover A: $12\text{ m/s}$; Rover B: $8\text{ m/s}$

A delivery drone conducts a round-trip inspection flight along a straight corridor connecting Facility Alpha and Facility Beta, which are separated by a distance of 36 km. The drone maintains a constant airspeed of 30 km/h relative to the surrounding air, requiring 2.4 h for the full round trip on a calm day. On a windy day, a steady wind blows at 10 km/h directly from Facility Alpha toward Facility Beta throughout the entire flight. What is the total flight time for the complete round trip on the windy day, and how does it compare to the calm-day flight time?

A) 2.7 h, which is 0.3 h longer than on a calm day

B) 2.4 h, which is identical to the calm-day flight time

C) 2.5 h, which is 0.1 h longer than on a calm day

D) 3.0 h, which is 0.6 h longer than on a calm day

A mobile weather station travels along a straight horizontal road due east at a constant speed of 16 m/s relative to the ground. An onboard anemometer measures the apparent velocity of the wind relative to the vehicle to be 20 m/s, directed 53° west of north. Based on these measurements, what are the speed and direction of the true wind relative to the ground? (Take $\sin 53^\circ = 0.8$ and $\cos 53^\circ = 0.6$.)

B) 20 m/s, directed 53° west of north

A maritime research station monitors two autonomous surface vessels, ASV-Alpha and ASV-Beta, traveling across calm open water. ASV-Alpha cruises due north at a constant speed of 8.0 m/s relative to the ocean floor, while ASV-Beta travels at a constant speed of 10.0 m/s relative to the ocean floor. An onboard tracking system on ASV-Alpha determines that ASV-Beta is moving directly due east relative to ASV-Alpha. What is the speed of ASV-Beta relative to ASV-Alpha, and in what direction is ASV-Beta moving relative to the ocean floor? (Take $\sin 53^\circ \approx 0.8$ and $\cos 53^\circ \approx 0.6$.)

C) 12.8 m/s; 53° north of east

At an automated freight terminal, a rail-mounted gantry crane travels due east along straight horizontal tracks at a constant speed of 3.0 m/s relative to the ground. Simultaneously, a motorized trolley moves along the crane's overhead girder due north at a constant speed of 4.0 m/s relative to the crane, while lowering an inspection sensor vertically downward at a constant speed of 12.0 m/s relative to the trolley. Based on these reference frames, what are the sensor's horizontal speed and its total speed relative to the ground?

A) Horizontal speed: 7.0 m/s; Total speed: 19.0 m/s

B) Horizontal speed: 5.0 m/s; Total speed: 17.0 m/s

C) Horizontal speed: 5.0 m/s; Total speed: 13.0 m/s

D) Horizontal speed: 1.0 m/s; Total speed: 11.0 m/s

To evaluate an automated tracking system, two unmanned surface vessels depart simultaneously from a harbor facility. Vessel 1 travels at a constant speed of 10 m/s in a direction 60° north of east relative to the stationary shore station. Vessel 2 moves due east at a constant speed of 5.0 m/s relative to the same shore station. From the reference frame of Vessel 2, what are the magnitude and direction of the velocity of Vessel 1? (Take $\sin 60^\circ = \frac{\sqrt{3}}{2}$ and $\cos 60^\circ = 0.5$.)

A) $5\sqrt{3}\text{ m/s}$ due north

C) $5\sqrt{3}\text{ m/s}$ at 30° north of east

D) 15 m/s at 60° north of east

An automated water-quality monitoring boat travels along a straight stretch of a river between two fixed sensor stations separated by a distance of 1200 m. Moving downstream with the current, the boat covers the distance in 200 s, whereas returning upstream against the current, it covers the same distance in 600 s. Assuming the boat maintains a constant speed relative to the water and the river flows at a uniform speed relative to the riverbank, what are the boat's speed relative to the water and the speed of the river current relative to the riverbank?

A) Boat speed: 6 m/s; Current speed: 2 m/s

B) Boat speed: 5 m/s; Current speed: 1 m/s

C) Boat speed: 4 m/s; Current speed: 2 m/s

D) Boat speed: 3 m/s; Current speed: 1 m/s

An autonomous aerial drone cruises horizontally due north at a constant speed of 15 m/s relative to the ground while tracking an uncrewed delivery cart. From the drone's frame of reference, the delivery cart is moving at a velocity of 20 m/s due west. At the same instant, a ground rover travels due west at a constant speed of 20 m/s relative to the ground along a parallel route. What is the delivery cart's speed relative to the ground, and what is its velocity relative to the ground rover?

A) 25 m/s, and 15 m/s due north

B) 25 m/s, and 15 m/s due south

C) 35 m/s, and 15 m/s due north

A river flows steadily due south at a speed of 3.0 m/s relative to the riverbank. A search-and-rescue boat needs to cross straight across the river along a path directed due east relative to the bank. If the boat moves at a constant speed of 5.0 m/s relative to the water, what is the magnitude of the boat's velocity relative to the riverbank, and in which direction must the boat be steered relative to east?

A) 5.8 m/s, steered south of east

C) 4.0 m/s, steered north of east

D) 4.0 m/s, steered south of east

On a horizontal testing facility, an autonomous vehicle, Car X, travels due east at a constant speed of 12 m/s relative to the ground. At the same time, another autonomous vehicle, Car Y, travels along a perpendicular track due north at a constant speed of 16 m/s relative to the ground. To calibrate Car X's onboard tracking system, what are the magnitude and direction of the velocity of Car Y relative to Car X?

A) 20 m/s, directed approximately 53° north of east

B) 28 m/s, directed approximately 37° north of west

C) 20 m/s, directed approximately 53° north of west

D) 28 m/s, directed approximately 53° south of west

Two automated inspection rovers, Rover A and Rover B, travel along the straight deck of a transport ship cruising due north at $15\text{ m/s}$ relative to the ocean water. Rover A drives due north at $4\text{ m/s}$ relative to the deck, while Rover B drives due south at $3\text{ m/s}$ relative to the deck. Based on these measurements, what are the velocity of Rover A relative to a stationary buoy anchored in the water and the velocity of Rover A relative to Rover B?

A) $11\text{ m/s}$ north relative to the buoy, and $1\text{ m/s}$ north relative to Rover B

B) $19\text{ m/s}$ north relative to the buoy, and $1\text{ m/s}$ north relative to Rover B

C) $19\text{ m/s}$ north relative to the buoy, and $7\text{ m/s}$ north relative to Rover B

D) $22\text{ m/s}$ north relative to the buoy, and $7\text{ m/s}$ south relative to Rover B

Relative motion Transitional Reasoning Practice

Physics · Motion · Physics · Describing Motion

20 Physics practice questions on Relative motion. Questions that build towards applied reasoning.

Layout:

Choose how questions appear in the preview and test.

Preview the questions below, then start to answer and see your results.

Questions

1.
While conducting an environmental survey along a straight river, an automated research boat heading upstream passes an unpowered data buoy drifting freely with the current at a fixed sensor station. The boat continues cruising upstream at a constant speed relative to the water for 30 minutes, then instantly turns around and travels downstream at the same speed relative to the water until it overtakes the drifting buoy 3.0 km downstream from the station. Assuming the river current flows at a uniform speed relative to the riverbank, what are the total time elapsed from the initial encounter until the boat overtakes the buoy and the speed of the river current relative to the riverbank?
- A) Total time: 60 minutes; speed of current: 3.0 km/h
- B) Total time: 45 minutes; speed of current: 4.0 km/h
- C) Total time: 30 minutes; speed of current: 6.0 km/h
- D) Total time: 90 minutes; speed of current: 2.0 km/h
2.
In an automated logistics center, an inclined straight conveyor ramp of length 72 m transports cargo between two workstations. During a system diagnostic, an autonomous inspection cart travels up the ramp in 60 s when the conveyor belt is stationary, whereas when the cart remains parked on the moving belt, the belt carries it to the top in 40 s. During regular operations, the cart drives up the ramp at its calibrated speed while the conveyor belt simultaneously runs upward at its operating speed. How much time does the cart take to traverse the ramp during regular operations, and what is the speed of the cart relative to the workstation floor?
- A) 24 s and 3.0 m/s
- B) 50 s and 1.44 m/s
- C) 20 s and 3.6 m/s
- D) 24 s and 0.6 m/s
3.
A flatbed transport vehicle travels along a straight horizontal track due east at a constant speed of 16 m/s relative to the ground. An automated launcher mounted on the flatbed releases a sensor capsule horizontally at a speed of 12 m/s due north relative to the vehicle. Simultaneously, a mobile camera rover travels along a parallel lane due east at a constant speed of 11 m/s relative to the ground. What are the speed of the sensor capsule relative to the ground and its speed relative to the camera rover immediately after launch?
- A) 20 m/s and 13 m/s
- B) 20 m/s and 9 m/s
- C) 28 m/s and 17 m/s
- D) 20 m/s and 25 m/s
4.
Two automated test rovers, Rover A and Rover B, travel at constant speeds around a closed circular track with a circumference of 600 m. When the rovers travel in opposite directions, they encounter each other every 30 s. When they travel in the same direction, Rover A overtakes Rover B once every 150 s. What are the constant speeds of Rover A and Rover B relative to the track?
- A) Rover A: $16\text{ m/s}$ ; Rover B: $4\text{ m/s}$
- B) Rover A: $14\text{ m/s}$ ; Rover B: $6\text{ m/s}$
- C) Rover A: $10\text{ m/s}$ ; Rover B: $6\text{ m/s}$
- D) Rover A: $12\text{ m/s}$ ; Rover B: $8\text{ m/s}$
5.
A delivery drone conducts a round-trip inspection flight along a straight corridor connecting Facility Alpha and Facility Beta, which are separated by a distance of 36 km. The drone maintains a constant airspeed of 30 km/h relative to the surrounding air, requiring 2.4 h for the full round trip on a calm day. On a windy day, a steady wind blows at 10 km/h directly from Facility Alpha toward Facility Beta throughout the entire flight. What is the total flight time for the complete round trip on the windy day, and how does it compare to the calm-day flight time?
- A) 2.7 h, which is 0.3 h longer than on a calm day
- B) 2.4 h, which is identical to the calm-day flight time
- C) 2.5 h, which is 0.1 h longer than on a calm day
- D) 3.0 h, which is 0.6 h longer than on a calm day
6.
A motorized research boat crosses a straight, uniform stretch of a river with a width of 240 m. The river water flows steadily due east at a constant speed of 3.0 m/s relative to the riverbank, and the boat maintains a constant speed of 4.0 m/s relative to the water. To reach the opposite bank in the minimum possible time, the boat is steered in the optimal heading direction. What are the minimum time required to complete the crossing and the magnitude of the boat's total displacement relative to the riverbank?
- A) 48 s and 240 m
- B) 48 s and 300 m
- C) 60 s and 300 m
- D) 60 s and 180 m
7.
A mobile weather station travels along a straight horizontal road due east at a constant speed of 16 m/s relative to the ground. An onboard anemometer measures the apparent velocity of the wind relative to the vehicle to be 20 m/s, directed 53° west of north. Based on these measurements, what are the speed and direction of the true wind relative to the ground? (Take $\sin 53^\circ = 0.8$ and $\cos 53^\circ = 0.6$ .)
- A) 4.0 m/s, directed due north
- B) 20 m/s, directed 53° west of north
- C) 12 m/s, directed due south
- D) 12 m/s, directed due north
8.
An atmospheric research team monitors a data pod drifting horizontally with a uniform wind that blows due east at a constant speed of 15 m/s relative to the ground. At the moment tracking begins, a recovery helicopter is located 3600 m directly downwind (due east) of the pod at the same altitude. The helicopter flies in a straight horizontal line directly toward the drifting pod at a constant airspeed (speed relative to the air) of 45 m/s. Relative to the ground, what is the speed of the helicopter, and how much time elapses before it intercepts the pod?
- A) 30 m/s and 120 s
- B) 30 m/s and 80 s
- C) 60 m/s and 60 s
- D) 60 m/s and 80 s
9.
A central dispatch system in an automated facility monitors two transport units, Unit 1 and Unit 2, moving along perpendicular straight tracks toward an intersection. Unit 1 travels due east toward the intersection at a constant speed of 12 m/s, starting from 90 m west of the intersection at time t = 0. Concurrently, Unit 2 travels due north toward the intersection at a constant speed of 16 m/s, starting from 120 m south of the intersection at t = 0. What is the magnitude of the velocity of Unit 2 relative to Unit 1, and what is the straight-line distance between the two units at t = 5.0 s?
- A) 20 m/s and 50 m
- B) 28 m/s and 50 m
- C) 20 m/s and 70 m
- D) 4 m/s and 130 m
10.
A maritime research station monitors two autonomous surface vessels, ASV-Alpha and ASV-Beta, traveling across calm open water. ASV-Alpha cruises due north at a constant speed of 8.0 m/s relative to the ocean floor, while ASV-Beta travels at a constant speed of 10.0 m/s relative to the ocean floor. An onboard tracking system on ASV-Alpha determines that ASV-Beta is moving directly due east relative to ASV-Alpha. What is the speed of ASV-Beta relative to ASV-Alpha, and in what direction is ASV-Beta moving relative to the ocean floor? (Take $\sin 53^\circ \approx 0.8$ and $\cos 53^\circ \approx 0.6$ .)
- A) 6.0 m/s; 37° north of east
- B) 6.0 m/s; 53° north of east
- C) 12.8 m/s; 53° north of east
- D) 2.0 m/s; 37° north of east
11.
At an automated freight terminal, a rail-mounted gantry crane travels due east along straight horizontal tracks at a constant speed of 3.0 m/s relative to the ground. Simultaneously, a motorized trolley moves along the crane's overhead girder due north at a constant speed of 4.0 m/s relative to the crane, while lowering an inspection sensor vertically downward at a constant speed of 12.0 m/s relative to the trolley. Based on these reference frames, what are the sensor's horizontal speed and its total speed relative to the ground?
- A) Horizontal speed: 7.0 m/s; Total speed: 19.0 m/s
- B) Horizontal speed: 5.0 m/s; Total speed: 17.0 m/s
- C) Horizontal speed: 5.0 m/s; Total speed: 13.0 m/s
- D) Horizontal speed: 1.0 m/s; Total speed: 11.0 m/s
12.
To evaluate an automated tracking system, two unmanned surface vessels depart simultaneously from a harbor facility. Vessel 1 travels at a constant speed of 10 m/s in a direction 60° north of east relative to the stationary shore station. Vessel 2 moves due east at a constant speed of 5.0 m/s relative to the same shore station. From the reference frame of Vessel 2, what are the magnitude and direction of the velocity of Vessel 1? (Take $\sin 60^\circ = \frac{\sqrt{3}}{2}$ and $\cos 60^\circ = 0.5$ .)
- A) $5\sqrt{3}\text{ m/s}$ due north
- B) 5.0 m/s due north
- C) $5\sqrt{3}\text{ m/s}$ at 30° north of east
- D) 15 m/s at 60° north of east
13.
A weather-monitoring van drives along a straight horizontal road on a windless day while rain falls vertically downward at a constant speed relative to the ground. When the van moves at a constant speed of 15 m/s, an onboard sensor detects that the raindrops leave streaks on the side windows slanting at 45° to the vertical. If the driver then increases the van's cruising speed to a constant 20 m/s along the same road, what are the speed of the rain relative to the ground and the speed of the rain relative to the van at this new speed?
- A) 12 m/s and 20 m/s
- B) 15 m/s and 35 m/s
- C) 15 m/s and 25 m/s
- D) 20 m/s and 28 m/s
14.
An automated water-quality monitoring boat travels along a straight stretch of a river between two fixed sensor stations separated by a distance of 1200 m. Moving downstream with the current, the boat covers the distance in 200 s, whereas returning upstream against the current, it covers the same distance in 600 s. Assuming the boat maintains a constant speed relative to the water and the river flows at a uniform speed relative to the riverbank, what are the boat's speed relative to the water and the speed of the river current relative to the riverbank?
- A) Boat speed: 6 m/s; Current speed: 2 m/s
- B) Boat speed: 5 m/s; Current speed: 1 m/s
- C) Boat speed: 4 m/s; Current speed: 2 m/s
- D) Boat speed: 3 m/s; Current speed: 1 m/s
15.
A passenger train of length 180 m travels at a constant speed of 25 m/s along a straight track parallel to a freight train of length 220 m moving in the same direction at 15 m/s. At the initial instant, the front of the passenger train is exactly aligned with the rear of the freight train. How much time elapses before the rear of the passenger train completely clears the front of the freight train, and what total distance does the passenger train travel relative to the ground during this overtaking maneuver?
- A) 10 s and 250 m
- B) 40 s and 1000 m
- C) 40 s and 600 m
- D) 22 s and 550 m
16.
A straight moving walkway at an airport terminal is 120 m long and moves due east at a constant speed of 1.0 m/s relative to the stationary floor. Passenger A steps onto the walkway at its western entrance and walks due east at 1.5 m/s relative to the walkway surface, while at the exact same instant, Passenger B begins walking due west on the adjacent stationary floor from the eastern end at 1.5 m/s relative to the floor. How long after starting do the two passengers pass each other, and what is the speed of Passenger A relative to Passenger B?
- A) 30 s and 4.0 m/s
- B) 40 s and 3.0 m/s
- C) 60 s and 2.0 m/s
- D) 48 s and 2.5 m/s
17.
An autonomous aerial drone cruises horizontally due north at a constant speed of 15 m/s relative to the ground while tracking an uncrewed delivery cart. From the drone's frame of reference, the delivery cart is moving at a velocity of 20 m/s due west. At the same instant, a ground rover travels due west at a constant speed of 20 m/s relative to the ground along a parallel route. What is the delivery cart's speed relative to the ground, and what is its velocity relative to the ground rover?
- A) 25 m/s, and 15 m/s due north
- B) 25 m/s, and 15 m/s due south
- C) 35 m/s, and 15 m/s due north
- D) 25 m/s, and 40 m/s due west
18.
A river flows steadily due south at a speed of 3.0 m/s relative to the riverbank. A search-and-rescue boat needs to cross straight across the river along a path directed due east relative to the bank. If the boat moves at a constant speed of 5.0 m/s relative to the water, what is the magnitude of the boat's velocity relative to the riverbank, and in which direction must the boat be steered relative to east?
- A) 5.8 m/s, steered south of east
- B) 2.0 m/s, steered due east
- C) 4.0 m/s, steered north of east
- D) 4.0 m/s, steered south of east
19.
On a horizontal testing facility, an autonomous vehicle, Car X, travels due east at a constant speed of 12 m/s relative to the ground. At the same time, another autonomous vehicle, Car Y, travels along a perpendicular track due north at a constant speed of 16 m/s relative to the ground. To calibrate Car X's onboard tracking system, what are the magnitude and direction of the velocity of Car Y relative to Car X?
- A) 20 m/s, directed approximately 53° north of east
- B) 28 m/s, directed approximately 37° north of west
- C) 20 m/s, directed approximately 53° north of west
- D) 28 m/s, directed approximately 53° south of west
20.
Two automated inspection rovers, Rover A and Rover B, travel along the straight deck of a transport ship cruising due north at $15\text{ m/s}$ relative to the ocean water. Rover A drives due north at $4\text{ m/s}$ relative to the deck, while Rover B drives due south at $3\text{ m/s}$ relative to the deck. Based on these measurements, what are the velocity of Rover A relative to a stationary buoy anchored in the water and the velocity of Rover A relative to Rover B?
- A) $11\text{ m/s}$ north relative to the buoy, and $1\text{ m/s}$ north relative to Rover B
- B) $19\text{ m/s}$ north relative to the buoy, and $1\text{ m/s}$ north relative to Rover B
- C) $19\text{ m/s}$ north relative to the buoy, and $7\text{ m/s}$ north relative to Rover B
- D) $22\text{ m/s}$ north relative to the buoy, and $7\text{ m/s}$ south relative to Rover B

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

Motion · Physics

Explore your next topic

Choose a topic and keep learning.

Transitional Reasoning
Acceleration Practice
Transitional Reasoning
Acceleration–time graphs Practice
Transitional Reasoning
Frames of reference Practice
Transitional Reasoning
Position, distance and displacement Practice
Transitional Reasoning
Position–time graphs Practice
Transitional Reasoning
Speed and velocity Practice
Transitional Reasoning
Velocity–time graphs Practice
Transitional Reasoning
Constant acceleration equations Practice
Transitional Reasoning
Constant velocity motion Practice
Transitional Reasoning
Free fall Practice
Transitional Reasoning
Graph slopes and areas Practice
Transitional Reasoning
Kinematics with calculus Practice

AI study assistant

Practice questions

Topic explanations

Download question PDFs

Relative motion Transitional Reasoning Practice

Questions

Quick Links

Terms of Service

Unlock the power of AI

AI study assistant

Practice questions

Topic explanations

Download question PDFs

Provide additional feedback

Why do you like this response?

Provide your feedback

Share

Questions