River Boat Problem — JEE Main Physics MCQs with Solutions
Free JEE Main 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 heads perpendicular to the current, which flows at 5 m/s. How long does the boat take to reach the opposite bank?
A. 48 s
B. 40 s
C. 25 s
D. 30 s ✓ Correct
Solution: The current does not affect the motion across the river: t = width/boat speed = 240/8 = 30 s.
Q2 — River Boat Problem · easy · numerical
A boat with still-water speed 8 m/s heads perpendicular to the banks of a 200 m wide river flowing at 15 m/s. How far downstream from the point directly opposite does it land?
A. 300 m
B. 375 m ✓ Correct
C. 160 m
D. 200 m
Solution: Crossing time t = 200/8 = 25 s; drift = river speed × time = 15 × 25 = 375 m.
Q3 — River Boat Problem · easy · numerical
A boat can move at 20 km/h in still water. It heads straight across a river flowing at 21 km/h. The resultant speed of the boat is:
A. 41 km/h
B. 21 km/h
C. 29 km/h ✓ Correct
D. 24.5 km/h
Solution: The two velocities are perpendicular: v = √(20² + 21²) = √(400 + 441) = √841 = 29 km/h.
Q4 — River Boat Problem · easy · numerical
A motorboat can travel at 24 km/h in still water. The river flows at 7 km/h. How long does the boat take to go 62 km downstream?
A. 2 h ✓ Correct
B. 1.5 h
C. 3.6 h
D. 2.6 h
Solution: Downstream speed = 24 + 7 = 31 km/h; t = 62/31 = 2 h.
Q5 — River Boat Problem · easy · numerical
A boat whose speed in still water is 20 km/h has to travel 36 km upstream in a river flowing at 8 km/h. The time taken is:
A. 2.5 h
B. 1.8 h
C. 1.3 h
D. 3 h ✓ Correct
Solution: Upstream speed = 20 − 8 = 12 km/h; t = 36/12 = 3 h.
Q6 — River Boat Problem · easy · numerical
A boat can move at 17 km/h in still water in a river flowing at 8 km/h. If it crosses along the shortest path (straight across), its resultant speed is:
A. 9 km/h
B. 17 km/h
C. 15 km/h ✓ Correct
D. 25 km/h
Solution: For the shortest path the upstream heading component cancels the current, so v = √(17² − 8²) = √225 = 15 km/h.
Q7 — River Boat Problem · medium · numerical
A boatman can row at 8 km/h in still water in a river flowing at 17 km/h. The river is 400 m wide. The minimum possible drift when he crosses is:
A. 400 m
B. 850 m
C. 500 m
D. 750 m ✓ Correct
Solution: When v_river > v_boat, minimum drift = d√(v_r² − v_b²)/v_b = 400 × √(289 − 64)/8 = 400 × 15/8 = 750 m.
Q8 — River Boat Problem · medium · numerical
A boat with still-water speed 12 km/h is in a river flowing at 24 km/h. To suffer minimum drift while crossing, at what angle upstream from the line straight across should the boat head?
A. 60°
B. 30° ✓ Correct
C. 37°
D. 45°
Solution: For v_river > v_boat, minimum drift occurs when sin θ = v_b/v_r = 12/24 = 1/2 ⇒ θ = 30° upstream of the perpendicular.
Q9 — River Boat Problem · medium · numerical
A motorboat with still-water speed 20 m/s crosses a 240 m wide river flowing at 7 m/s, heading 37° upstream from the line straight across (cos 37° = 0.8). The time to cross is:
A. 15 s ✓ Correct
B. 30 s
C. 20 s
D. 12 s
Solution: Component across the river = 20 cos 37° = 16 m/s; t = 240/16 = 15 s.
Q10 — River Boat Problem · medium · numerical
A boat with still-water speed 20 m/s crosses a 120 m wide river flowing at 12 m/s, heading 53° upstream from the line straight across (sin 53° = 0.8). Find the drift when it reaches the other bank.
A. 120 m downstream
B. 40 m downstream
C. Zero
D. 40 m upstream ✓ Correct
Solution: Across component = 20 cos 53° = 12 m/s ⇒ t = 120/12 = 10 s; net stream-wise velocity = 12 − 20 sin 53° = −4 m/s, so the boat lands 4 × 10 = 40 m upstream.
Q11 — River Boat Problem · medium · numerical
A boat that moves at 25 km/h in still water crosses a 1.2 km wide river along the shortest path. The river flows at 7 km/h. The crossing time is:
A. 2.3 min
B. 4 min
C. 3 min ✓ Correct
D. 2.9 min
Solution: Resultant speed along the shortest path = √(25² − 7²) = 24 km/h; t = 1.2/24 h = 0.05 h = 3 min.
Q12 — River Boat Problem · medium · numerical
A boat with still-water speed 20 km/h must reach the point directly opposite on the other bank of a 4 km wide river flowing at 12 km/h (sin 37° = 0.6). What should it do?
A. Head 53° upstream from the perpendicular; crossing time 15 min
B. Head 37° upstream from the perpendicular; crossing time 15 min ✓ Correct
C. Head 30° upstream from the perpendicular; crossing time 20 min
D. Head 37° upstream from the perpendicular; crossing time 12 min
Solution: sin θ = v_r/v_b = 12/20 = 0.6 ⇒ θ = 37° upstream; resultant speed across = 20 cos 37° = 16 km/h, so t = 4/16 h = 15 min.
Q13 — River Boat Problem · medium · numerical
A swimmer crosses a river in 15 min when swimming perpendicular to the current, and in 17 min when crossing along the shortest path. The ratio of the river speed to his swimming speed is:
A. 15 : 17
B. 8 : 15
C. 17 : 8
D. 8 : 17 ✓ Correct
Solution: Width d = v_s × 15 = √(v_s² − v_r²) × 17; squaring gives 225 v_s² = 289(v_s² − v_r²) ⇒ v_r²/v_s² = 64/289, so v_r : v_s = 8 : 17.
Q14 — River Boat Problem · medium · numerical
A speedboat crosses a 600 m wide river in 24 s when it heads straight across, and in 25 s when it travels along the shortest path. The speed of the river current is:
A. 25 m/s
B. 7 m/s ✓ Correct
C. 1 m/s
D. 24 m/s
Solution: Still-water speed = 600/24 = 25 m/s; shortest-path resultant = 600/25 = 24 m/s; v_r = √(25² − 24²) = √49 = 7 m/s.
Q15 — River Boat Problem · medium · numerical
A boat with still-water speed 17 km/h ferries across a 2 km wide river flowing at 15 km/h, going straight across and straight back along the shortest path. The total time for the round trip is:
A. 16 min
B. 60 min
C. 14 min
D. 30 min ✓ Correct
Solution: Speed along the shortest path each way = √(17² − 15²) = √64 = 8 km/h; T = 2 × 2/8 h = 0.5 h = 30 min.
Q16 — River Boat Problem · medium · numerical
A boat crosses a river in minimum time by heading straight across at its still-water speed of 12 m/s. The current of 7 m/s carries it 175 m downstream. The width of the river is:
A. 250 m
B. 300 m ✓ Correct
C. 175 m
D. 420 m
Solution: Crossing time t = drift/current = 175/7 = 25 s; width = 12 × 25 = 300 m.
Q17 — River Boat Problem · medium · numerical
A boat crosses a 300 m wide river along the shortest path in 20 s. If the current flows at 8 m/s, the speed of the boat in still water is:
A. 15 m/s
B. 17 m/s ✓ Correct
C. 13 m/s
D. 23 m/s
Solution: Resultant speed along the shortest path = 300/20 = 15 m/s; still-water speed = √(15² + 8²) = √289 = 17 m/s.
Q18 — River Boat Problem · medium · numerical
A boat with still-water speed 20 km/h heads at 53° upstream from the line straight across a river flowing at 16 km/h (sin 53° = 0.8). The magnitude of its resultant (ground) velocity is:
A. 4 km/h
B. 36 km/h
C. 12 km/h ✓ Correct
D. 16 km/h
Solution: The upstream component 20 sin 53° = 16 km/h exactly cancels the current, leaving only the across component 20 cos 53° = 12 km/h.
Q19 — River Boat Problem · medium · numerical
A motorboat moves at 21 km/h in still water. It travels 30 km downstream in a river flowing at 9 km/h and returns to the starting point. The total time for the round trip is:
A. 3.5 h ✓ Correct
B. 4.5 h
C. 2.9 h
D. 3 h
Solution: Downstream: 30/(21 + 9) = 1 h; upstream: 30/(21 − 9) = 2.5 h; total = 3.5 h.
Q20 — River Boat Problem · medium · numerical
A boat with still-water speed 40 km/h crosses a 3.2 km wide river flowing at 8 km/h, heading 37° downstream from the line straight across (sin 37° = 0.6). How far downstream from the starting point does it land?
A. 0.8 km
B. 3.2 km ✓ Correct
C. 2.4 km
D. 1.6 km
Solution: Across component = 40 cos 37° = 32 km/h ⇒ t = 3.2/32 = 0.1 h; downstream speed = 40 sin 37° + 8 = 24 + 8 = 32 km/h, so drift = 32 × 0.1 = 3.2 km.