First slide

Simple hormonic motion

Question

The minimum time required for a boat to cross a river is 30 min and the time required for the boat to cross the same river in the shortest possible path is 50 min. In both cases velocity of boat relative to still water is ‘V’ and velocity of water is ‘u’. Then $\frac{u}{v}$ is ______

Moderate

A

$\frac{5}{4}$
B

$\frac{2}{3}$
C

$\frac{4}{5}$
D

$\frac{3}{5}$

Solution

$\begin{array}{l} \frac{d}{v} = t_{\min} = 30 ....... (1) \\ A l o n g t h e s h o r t e s t p o s s i b l e p a t h, \frac{d}{\sqrt{v^{2} - u^{2}}} = 50 ....... (2) \\ ∴ \frac{\sqrt{v^{2} - u^{2}}}{V} = \frac{30}{50} \Rightarrow \frac{u}{v} = \frac{4}{5} . \end{array}$

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