Question

A swimmer can swim with velocity of $12\text{km/h}$ in still water. Water flowing in a river has velocity $6\text{km/h}$. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ${}^{\circ }$. (Round off to the Nearest Integer) (Find the angle in degree)

Answer 1

Angle of direction of swimmer with respect to direction of flow of river water is shown in the below diagram.


Given, $V_m=12\text{km/h}$ and $V_r=6\text{km/h}$

In order to reach the just opposite point on the other bank, the velocity of the swimmer should be perpendicular to the direction of flow of river water with respect to ground.

So, the horizontal component of swimmer velocity should be equal and opposite to the velocity of the river.

$\Rightarrow V_m\sin \theta =v_r$

$\Rightarrow \sin \theta =\frac{6}{12}=\frac{1}{2}$

$\Rightarrow \theta ={30}^{\circ }$

$\because \alpha ={90}^{\circ }+\theta$

$\therefore \alpha ={120}^{\circ }$