A boat crosses a river from one bank A to another bank B which is… | MHT CET 2026 (20 Apr, Shift 1)

Q1MHT CET 2026 · 20 APR · SHIFT 1Medium

Relative Velocity in Two Dimensions

A boat crosses a river from one bank A to another bank B which is opposite. The distance between them is D. The speed of water is $V_W$ and that of boat relative to water is $V_B$ . If $V_B = 2V_W$ , the time taken by the boat to cross the river directly along AB is $\left(\sin 30^\circ = \frac{1}{2}\right) \cdot \left(\cos 30^\circ = \frac{\sqrt{3}}{2}\right)$

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Answer: (c)

To go straight along AB, head upstream at $\phi$ from AB: $\sin\phi = \frac{V_W}{V_B} = \frac{1}{2} \Rightarrow \phi = 30^\circ$
Speed along AB $= V_B\cos 30^\circ = \frac{\sqrt{3}}{2}V_B$
$t = \frac{D}{\frac{\sqrt{3}}{2}V_B} = \frac{2D}{V_B\sqrt{3}}$
So the answer is (c).

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Relative Velocity in Two Dimensions question from MHT CET 2026 (20 Apr, Shift 1)

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