River Boat Problem — IISER Physics MCQs with Solutions
Free IISER 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 motorboat can move at 12 m/s in still water. It crosses a river 180 m wide by heading straight across (perpendicular to the current). What is the minimum time to cross?
A. 15 s ✓ Correct
B. 25 s
C. 20 s
D. 9 s
Solution: Minimum crossing time uses the full still-water speed across the river: t = 180/12 = 15 s.
Q2 — River Boat Problem · easy · numerical
A boat heads straight across a 240 m wide river at 12 m/s (its still-water speed). The current flows at 9 m/s. How far downstream does the boat land?
A. 300 m
B. 120 m
C. 240 m
D. 180 m ✓ Correct
Solution: Crossing time t = 240/12 = 20 s; drift = current × time = 9 × 20 = 180 m.
Q3 — River Boat Problem · easy · numerical
A ferry heads straight across a river at 24 km/h while the current flows at 10 km/h. What is the ferry’s resultant speed with respect to the ground?
A. 20 km/h
B. 14 km/h
C. 26 km/h ✓ Correct
D. 34 km/h
Solution: The two velocities are perpendicular: v = √(24² + 10²) = √676 = 26 km/h.
Q4 — River Boat Problem · easy · numerical
A boat can travel at 15 km/h in still water in a river flowing at 9 km/h. At what angle upstream from the straight-across direction must it head to reach the point exactly opposite? (sin 37° = 0.6)
A. 37° upstream of the straight-across direction ✓ Correct
B. 53° upstream of the straight-across direction
C. 30° upstream of the straight-across direction
D. 45° upstream of the straight-across direction
Solution: For zero drift, sinθ = v(river)/v(boat) = 9/15 = 0.6 ⇒ θ = 37° upstream of the line straight across.
Q5 — River Boat Problem · easy · numerical
A boat with still-water speed 34 km/h crosses a river flowing at 16 km/h along the shortest path (landing directly opposite). What is its speed relative to the ground during the crossing?
A. 24 km/h
B. 18 km/h
C. 30 km/h ✓ Correct
D. 50 km/h
Solution: On the shortest path the ground speed is √(v(boat)² − v(river)²) = √(34² − 16²) = √900 = 30 km/h.
Q6 — River Boat Problem · easy · numerical
A boat heading straight across a river reaches the far bank in 30 s, but lands 120 m downstream of its starting point. What is the speed of the current?
A. 3 m/s
B. 6 m/s
C. 5 m/s
D. 4 m/s ✓ Correct
Solution: The drift is caused entirely by the current: v(river) = 120/30 = 4 m/s.
Q7 — River Boat Problem · easy · numerical
A kayaker paddles at 15 km/h in still water. She travels 40 km downstream in a river flowing at 5 km/h. How long does the trip take?
A. 4 h
B. 2 h ✓ Correct
C. 3 h
D. 2 h 40 min
Solution: Downstream speed = 15 + 5 = 20 km/h, so t = 40/20 = 2 h.
Q8 — River Boat Problem · easy · numerical
A swimmer heads straight across a 90 m wide river at 1.8 m/s while the current is 2.4 m/s. What is the magnitude of her total displacement when she reaches the far bank?
A. 210 m
B. 120 m
C. 90 m
D. 150 m ✓ Correct
Solution: Crossing time t = 90/1.8 = 50 s gives drift = 2.4 × 50 = 120 m; displacement = √(90² + 120²) = √22500 = 150 m.
Q9 — River Boat Problem · medium · numerical
A boat can move at 2.5 m/s in still water. It crosses a 300 m wide river flowing at 1.5 m/s along the shortest path (landing directly opposite). How long does the crossing take?
A. 100 s
B. 120 s
C. 200 s
D. 150 s ✓ Correct
Solution: Effective speed across = √(2.5² − 1.5²) = √4 = 2 m/s, so t = 300/2 = 150 s.
Q10 — River Boat Problem · medium · numerical
A launch with still-water speed 25 km/h must land exactly opposite its starting point on a river flowing at 20 km/h. At what angle upstream from the straight-across direction must it be steered? (sin 53° = 0.8)
A. 53° upstream of the straight-across direction ✓ Correct
B. 45° upstream of the straight-across direction
C. 60° upstream of the straight-across direction
D. 37° upstream of the straight-across direction
Solution: sinθ = v(river)/v(boat) = 20/25 = 0.8 ⇒ θ = 53° upstream of the line straight across.
Q11 — River Boat Problem · medium · numerical
A boat whose still-water speed is 25 km/h heads at 37° upstream of the straight-across direction in a river flowing at 15 km/h. The river is 5 km wide. How long does it take to reach the opposite bank? (sin 37° = 0.6, cos 37° = 0.8)
A. 25 min
B. 20 min
C. 12 min
D. 15 min ✓ Correct
Solution: The upstream component 25 sin 37° = 15 km/h exactly cancels the current, leaving 25 cos 37° = 20 km/h straight across; t = 5/20 h = 15 min.
Q12 — River Boat Problem · medium · numerical
A boat’s still-water speed is 26 km/h and the river flows at 10 km/h. Find the ratio of the time taken to cross by heading straight across (minimum time) to the time taken along the shortest path.
A. 5 : 13
B. 12 : 13 ✓ Correct
C. 5 : 12
D. 13 : 12
Solution: t(min) = d/26 and t(shortest) = d/√(26² − 10²) = d/24, so t(min) : t(shortest) = 24 : 26 = 12 : 13.
Q13 — River Boat Problem · medium · numerical
A boat crosses a 300 m wide river in 15 s when it heads straight across, but needs 25 s when it steers to land directly opposite. What is the speed of the current?
A. 16 m/s ✓ Correct
B. 20 m/s
C. 12 m/s
D. 8 m/s
Solution: Still-water speed = 300/15 = 20 m/s and shortest-path ground speed = 300/25 = 12 m/s, so v(river) = √(20² − 12²) = √256 = 16 m/s.
Q14 — River Boat Problem · medium · numerical
A swimmer can swim at 1.5 m/s in still water, but the river flows at 2.5 m/s and is 90 m wide. What is the minimum possible downstream drift while crossing?
A. 60 m
B. 120 m ✓ Correct
C. 90 m
D. 150 m
Solution: When the current beats the swimmer, minimum drift = d√(v(river)² − v(swim)²)/v(swim) = 90 × √(6.25 − 2.25)/1.5 = 90 × 2/1.5 = 120 m.
Q15 — River Boat Problem · medium · numerical
A motorboat with still-water speed 20 km/h goes to a village 30 km downstream and returns. The river flows at 10 km/h. What is the total time for the round trip?
A. 3 h
B. 4 h ✓ Correct
C. 5 h
D. 2 h
Solution: Downstream: 30/(20 + 10) = 1 h; upstream: 30/(20 − 10) = 3 h; total = 4 h.
Q16 — River Boat Problem · medium · numerical
A boat heads straight across a 480 m wide river at 16 m/s while the current flows at 12 m/s. What is the magnitude of the boat’s displacement when it reaches the far bank?
A. 840 m
B. 480 m
C. 360 m
D. 600 m ✓ Correct
Solution: Crossing time t = 480/16 = 30 s gives drift = 12 × 30 = 360 m; displacement = √(480² + 360²) = √360000 = 600 m.
Q17 — River Boat Problem · medium · numerical
A launch heads straight across a river at 28 km/h while the current is 21 km/h. What angle does its actual path over the ground make with the straight-across direction?
A. tan⁻¹(3/4) ≈ 37° ✓ Correct
B. tan⁻¹(4/3) ≈ 53°
C. 30°
D. 45°
Solution: tanθ = v(river)/v(boat) = 21/28 = 3/4, so the track is inclined ≈ 37° downstream of the straight-across line.
Q18 — River Boat Problem · medium · numerical
A kayaker who paddles at 12 km/h in still water goes 27 km upstream in a river flowing at 3 km/h. How long does the upstream journey take?
A. 9 h
B. 2.25 h
C. 1.8 h
D. 3 h ✓ Correct
Solution: Upstream speed = 12 − 3 = 9 km/h, so t = 27/9 = 3 h.
Q19 — River Boat Problem · medium · numerical
A swimmer heads straight across a 100 m wide river at 1.0 m/s while the current flows at 2.4 m/s. What distance does she actually travel (along her straight ground path) before reaching the far bank?
A. 260 m ✓ Correct
B. 240 m
C. 100 m
D. 340 m
Solution: Crossing time t = 100/1.0 = 100 s and ground speed = √(1.0² + 2.4²) = 2.6 m/s, so path length = 2.6 × 100 = 260 m.
Q20 — River Boat Problem · medium · numerical
A pilot points his boat 30° upstream of the straight-across direction and finds he lands exactly opposite his starting point. The current is 10 km/h. What is the boat’s speed in still water?
A. 20 km/h ✓ Correct
B. 30 km/h
C. 10√3 ≈ 17.3 km/h
D. 5 km/h
Solution: Zero drift requires v(boat) sin 30° = v(river), so v(boat) = 10/0.5 = 20 km/h.