Question

A swimmer wishes to cross a $500m$ wide river flowing at $5kmph$ this speed with respect to water is $3kmph$. If he heads in a direction making an angle $\theta$ with the flow, the time he takes to cross the river.

• A. $\frac{10}{\sin \theta }$ minutes
• B. $10\cos \theta$ minutes
• C. $10\sec \theta$ minutes
• D. $10$ minutes

Answer 1

The correct option is A $\frac{10}{\sin \theta }$ minutes

The velocity of man w.r.t water $=3kmph$

The breadth of river $=500m=0.5km$

Component of the velocity of man w.rt river along horizontal axis

$v=3\sin \theta$

Now time taken to cross the river

$t=\frac{Distance}{Velocityalonghorizontalaxis}$

$t=\frac{0.5}{3\sin \theta }hrs$

$t=\frac{0.5\times 60}{3\sin \theta }min$

$t=\frac{10}{\sin \theta }minutes$