Question

A person swims in a river aiming to reach exactly on the opposite point on the bank of river. His speed of swimming is $0.5m/s$ at an angle of ${120}^{\circ }$ with the direction of flow of water. The speed of water is

• A. $1.0m/s$
• B. $0.5m/s$
• C. $0.25m/s$
• D. $0.43m/s$

Answer 1

Answer: (C)

$0.25m/s$

The angle made by the person swimming with the direction perpendicular to the flow of water is ${120}^{\circ }-{90}^{\circ }={30}^{\circ }$

To reach the point B, drift must be zero, i.e., the relative velocity of boat w.r.t. river, $v_{br}$, should be along perpendicular direction.
Equating the component of velocity along horizontal direction to zero,
$v_b\sin \theta -v_r=0$

$\sin {30}^{\circ }=\frac{v_{water}}{0.5}$

or
$v_{water}=\frac{1}{2}\times 0.5=0.25m/s$