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A man directly crosses a river in time t...

A man directly crosses a river in time `t_1` and swims down the current a distance equal to the width of the river I time `t_2`. If `u and v` be the speed of the current and the man respectively, show that : `t_1 :t_2 = sqrt(v + u) : sqrt(v - u))`.

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To solve the problem, we need to analyze the motion of a man crossing a river and swimming downstream. Let's break it down step by step. ### Step 1: Define the variables Let: - \( d \) = width of the river - \( u \) = speed of the current - \( v \) = speed of the man in still water - \( t_1 \) = time taken to cross the river directly ...
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