First slide

Relative velocity in 1-d

Question

A man swimming downstream overcome a float at a point M. After travelling distance D he turned back and passed the float at a distance of D/2 from the point M, then the ratio of speed of swimmer with respect to still water to the speed of the river will be

Moderate

A

2
B

3
C

4
D

2.5

Solution

Time taken by man to go from M to P and then P to N = time taken by float to go from M to N.
$\begin{array}{l} \frac{D}{v + u} + \frac{D}{2 (v - u)} = \frac{D}{2 u} \\ Simplify to get \frac{v}{u} = 3 . \end{array}$

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