Question

A man wishes to cross a river in a boat. If he crosses the river in minimum time, then he takes $10$ minutes with a drift of $120m$ . If he crosses the river taking shortest path, he takes $12.5$ minutes. Velocity of boat w.r.t water is :

• A. $40m/min$
• B. $20m/min$
• C. $10m/min$
• D. $30m/min$

Answer 1

Answer: (B)

$20m/min$

Case:1 For minimum time

The time is given as,

$t_1=\frac{d}{v}$

$10=\frac{d}{v}$ (1)

The drift is given as,

$u\times t_1=120$

$u\times \left(10\times 60\right)=120$

$u=\frac{1}{5}m/s$

Case:1 For the shortest route

Let the angle with the river flow is $\angle A$.

The time is given as,

$t_2=\frac{d}{v\sin A}$

$12.5=\frac{d}{\sqrt{v^2-u^2}}$ (2)

Divide equation (2) in (1)

$\frac{10}{12.5}=\frac{d}{v\times \frac{d}{\sqrt{v^2-u^2}}}$

$\frac{4}{5}=\sqrt{1-\frac{\frac{1}{25}}{v^2}}$

$v=\frac{1}{3}m/s$

$v=20m/min$

The velocity of the boat with respect to water is $20m/min$.