River Boat Problem — NEET Physics MCQs with Solutions
Free NEET Physics River Boat Problem MCQs with step-by-step solutions (20 questions). Part of Motion in 2D. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — River Boat Problem · easy · numerical
A river is 240 m wide. A boat whose speed in still water is 8 m/s crosses the river in the minimum possible time. The minimum time taken is:
A. 60 s
B. 40 s
C. 30 s ✓ Correct
D. 24 s
Solution: For minimum time the boat heads straight across, so t = d/v_b = 240/8 = 30 s.
Q2 — River Boat Problem · easy · numerical
A boat heads straight across a 90 m wide river at 6 m/s while the current flows at 8 m/s. By the time it reaches the far bank, the boat has been carried downstream by:
A. 90 m
B. 60 m
C. 150 m
D. 120 m ✓ Correct
Solution: Crossing time t = 90/6 = 15 s; drift = 8 × 15 = 120 m.
Q3 — River Boat Problem · easy · numerical
A boat can move at 12 m/s in still water. It heads straight across a river flowing at 5 m/s. The magnitude of its resultant velocity is:
A. 17 m/s
B. 13 m/s ✓ Correct
C. 7 m/s
D. 12 m/s
Solution: v = √(12² + 5²) = √169 = 13 m/s.
Q4 — River Boat Problem · easy · numerical
A boat with still-water speed 10 m/s wants to reach the point exactly opposite on the far bank of a river flowing at 5 m/s. It must head upstream, measured from the line straight across, at an angle of:
A. 45°
B. 15°
C. 30° ✓ Correct
D. 60°
Solution: For zero drift, sinθ = v_river/v_boat = 5/10 = 1/2 ⇒ θ = 30°.
Q5 — River Boat Problem · easy · numerical
A boat with speed 13 m/s in still water crosses a 150 m wide river along the shortest path. If the current is 5 m/s, the crossing takes:
A. 10 s
B. 30 s
C. 12.5 s ✓ Correct
D. 11.5 s
Solution: Effective speed straight across = √(13² − 5²) = 12 m/s, so t = 150/12 = 12.5 s.
Q6 — River Boat Problem · easy · numerical
A boat heading straight across a 300 m wide river at 5 m/s lands 240 m downstream of the point directly opposite. The speed of the current is:
A. 3 m/s
B. 2 m/s
C. 4 m/s ✓ Correct
D. 5 m/s
Solution: Crossing time t = 300/5 = 60 s; current = drift/time = 240/60 = 4 m/s.
Q7 — River Boat Problem · easy · numerical
A river is 180 m wide. The minimum time in which a boat can cross it is 20 s. The speed of the boat in still water is:
A. 4.5 m/s
B. 12 m/s
C. 9 m/s ✓ Correct
D. 6 m/s
Solution: In minimum-time crossing the full still-water speed points across: v_b = 180/20 = 9 m/s.
Q8 — River Boat Problem · easy · numerical
A boat heads straight across a 30 m wide river at 6 m/s while the current is 8 m/s. The magnitude of the boat's displacement when it reaches the other bank is:
A. 70 m
B. 40 m
C. 30 m
D. 50 m ✓ Correct
Solution: t = 30/6 = 5 s gives a drift of 8 × 5 = 40 m; displacement = √(30² + 40²) = 50 m.
Q9 — River Boat Problem · easy · numerical
A swimmer can swim at 8 km/h in still water. He swims straight across a river flowing at 6 km/h. His speed with respect to the ground is:
A. 2 km/h
B. 7 km/h
C. 14 km/h
D. 10 km/h ✓ Correct
Solution: v = √(8² + 6²) = √100 = 10 km/h.
Q10 — River Boat Problem · easy · numerical
A swimmer whose still-water speed is 6 km/h wants to cross a 0.5 km wide river in the minimum time. The minimum time is:
A. 5 min ✓ Correct
B. 3 min
C. 10 min
D. 6 min
Solution: t = d/v = 0.5/6 h = 1/12 h = 5 min.
Q11 — River Boat Problem · easy · numerical
A boat with speed 20 m/s in still water crosses a river along the shortest path. If the current flows at 12 m/s, the boat's speed with respect to the ground is:
A. 8 m/s
B. 12 m/s
C. 20 m/s
D. 16 m/s ✓ Correct
Solution: Along the shortest path the ground speed is √(20² − 12²) = √256 = 16 m/s.
Q12 — River Boat Problem · easy · numerical
A swimmer heads straight across an 80 m wide river at 2 m/s. The current is 1.5 m/s. The distance he is carried downstream is:
A. 60 m ✓ Correct
B. 40 m
C. 80 m
D. 120 m
Solution: t = 80/2 = 40 s; drift = 1.5 × 40 = 60 m.
Q13 — River Boat Problem · medium · numerical
A boat's speed in still water is 10 m/s and the river flows at 8 m/s. The ratio of the time taken to cross while heading straight across (minimum time) to the time taken along the shortest path is:
A. 2 : 3
B. 3 : 5 ✓ Correct
C. 4 : 5
D. 5 : 3
Solution: t_min = d/10 while t_shortest = d/√(10² − 8²) = d/6, so t_min : t_shortest = 6 : 10 = 3 : 5.
Q14 — River Boat Problem · medium · numerical
A boat with still-water speed 8 km/h heads at 30° upstream from the line straight across a river flowing at 4 km/h. The magnitude of its resultant velocity is:
A. 4√3 ≈ 6.9 km/h ✓ Correct
B. 8 km/h
C. 4 km/h
D. 12 km/h
Solution: The upstream component 8 sin30° = 4 km/h exactly cancels the current, leaving 8 cos30° = 4√3 ≈ 6.9 km/h straight across.
Q15 — River Boat Problem · medium · numerical
To reach the point directly opposite, a boatman must point his boat at 60° upstream from the line straight across. If the boat's still-water speed is 6 m/s, the speed of the current is:
A. 6√3 ≈ 10.4 m/s
B. 1.5 m/s
C. 3 m/s
D. 3√3 ≈ 5.2 m/s ✓ Correct
Solution: Zero drift requires current = 6 sin60° = 3√3 ≈ 5.2 m/s.
Q16 — River Boat Problem · medium · numerical
A swimmer with still-water speed 10 km/h crosses a 1 km wide river along the shortest path. The current is 6 km/h. The time taken is:
A. 15 min
B. 6 min
C. 7.5 min ✓ Correct
D. 10 min
Solution: Speed straight across = √(10² − 6²) = 8 km/h; t = 1/8 h = 7.5 min.
Q17 — River Boat Problem · medium · numerical
A boat crosses a 360 m wide river along the shortest path in 30 s. If the current is 5 m/s, the speed of the boat in still water is:
A. 17 m/s
B. 13 m/s ✓ Correct
C. 12 m/s
D. 7 m/s
Solution: The across component is 360/30 = 12 m/s, so still-water speed = √(12² + 5²) = 13 m/s.
Q18 — River Boat Problem · medium · numerical
A boat heads straight across a river flowing at 4 m/s. Its resultant velocity makes an angle of 60° with the direction of the current. The boat's speed in still water is:
A. 2√3 ≈ 3.5 m/s
B. 4/√3 ≈ 2.3 m/s
C. 4√3 ≈ 6.9 m/s ✓ Correct
D. 8 m/s
Solution: tan60° = v_boat/v_river ⇒ v_boat = 4 tan60° = 4√3 ≈ 6.9 m/s.
Q19 — River Boat Problem · medium · numerical
A boat heads straight across a 160 m wide river at 8 m/s while the current is 6 m/s. The actual distance travelled by the boat along its path by the time it reaches the far bank is:
A. 260 m
B. 120 m
C. 200 m ✓ Correct
D. 160 m
Solution: t = 160/8 = 20 s and ground speed = √(8² + 6²) = 10 m/s, so path length = 10 × 20 = 200 m.
Q20 — River Boat Problem · medium · numerical
A boat's speed in still water is 6√2 ≈ 8.5 km/h and the river flows at 6 km/h. To land exactly opposite its starting point, the boat must head upstream from the straight-across direction at an angle of:
A. 15°
B. 45° ✓ Correct
C. 60°
D. 30°
Solution: sinθ = 6/(6√2) = 1/√2 ⇒ θ = 45°.