Question

A swimmer wishes to cross $500m$ wide river flowing at $3km/h$. His speed with respect to water is $5km/h$.

(a) If he heads in a direction making an angle of =${30}^{\circ }$ with the flow, find the time he takes to cross the river. Also find for = ${150}^{\circ }$ . (b) Find the shortest possible time to cross the river.

• A. $20min,20min,20min$
• B. $12min,12min,6min$
• C. $20min,40min,10min$
• D. $30min,20min,15min$

Answer 1

The correct option is B $12min,12min,6min$

(a) The river is $500m$ wide.

River flow velocity$=3km/hr$

Respective swimmer's velocity$=5km/hr$

From Figure-1, time$=\frac{w}{5\sin {30}^{\circ }}$

time$=\frac{1}{5}hour=12min$

For $\theta ={150}^{\circ }$ (Figure-2)

time$=\frac{\frac{1}{2}}{5\cos {60}^{\circ }}=12min$

(b) For shortest possible time, he must stock perpendicular to the flow of river.

So, time$=\frac{\frac{1}{2}}{5}hour=6min$