Question

Find the width of the river.

• A. $150m$
• B. $200m$
• C. $120m$
• D. $100m$

Answer 1

The correct option is B $200m$

Let$,$ $v_r=$ velocity of river

$v_{br}=$ velocity of river in still water

$w=$ width the river

Given$,$ $t_{min}=10minor\frac{w}{v_{br}}$---------------$\left(1\right)$

Drift in this case will be$,$

$x=v_{r}t$

$\therefore 120=10v_r$-------------------------$\left(2\right)$

Shortest path is taken when $v_b$ is along $AB.$ In this case$,$

$v_b=\sqrt{v_{br}^2-v_r^2}$

Now$,$ $12.5=\frac{w}{v_b}=\frac{w}{\sqrt{v_{br}^2-v_r^2}}$----------------$\left(3\right)$

solving these three equations$,$ we get

$v_{br}=20m/min,$ $v_r=12m/min$ and $w=200m.$

Hence,

option $\left(B\right)$ is correct answer.