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Relative Velocity in 2D

A river is 20...

Question

A river is 20 m wide. River speed is 3 m/s. A boat starts with velocity perpendicular to river current. Velocity of boat is 5 m/s. How far from the point directly opposite to the starting point does the boat reach the opposite bank?

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Solution

Let the horizontal drift of the boat at the opposite bank be $L$
Time taken by the boat to reach the opposite bank $t = \frac{d}{V_{b}}$
$⟹$ $t = \frac{20}{5} = 4$ s
$∴$ $L = V_{w} t = 3 \times 4 = 12 m$

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