A river flows from west to east with speed 9 km h⁻¹. A boat can move with maximum speed 27 km h⁻¹ in still water. It crosses the river in half a minute while moving at maximum speed at an angle 150° to the direction of river flow. The width of the river is:
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Question

A river flows from west to east with speed 9 km h⁻¹. A boat can move with maximum speed 27 km h⁻¹ in still water. It crosses the river in half a minute while moving at maximum speed at an angle 150° to the direction of river flow. The width of the river is:

Options

G1 Physics · Accepted Answer

The river velocity is along east-west, so it does not contribute to the component perpendicular to the river banks. The boat is directed at 150° to the river-flow direction, hence its cross-river component is v⊥ = 27 sin150° = 27×(1/2) = 13.5 km h⁻¹. Convert to m/s: 13.5 km h⁻¹ = 13.5×(5/18) = 3.75 m/s. Crossing time = 0.5 min = 30 s. Width, d = v⊥t = 3.75×30 = 112.5 m. Correct option: B.