Question

15. A swimmer crosses a river in shortest distance. If
he tries to swim at 4 km/hr maintaining 120° with
the downstream then speed of the river is
(1) 1 km/hr
(2) 2 km/hr
(3) 3 km/hr
(4) 4 km/hr​

Answer 1

Answer: 2km/h

Explanation:All the explanation is in the photo.

Answer 2

Answer:

The speed of the river is 2 km/hr.

(2) is correct option.

Explanation:

Given that,

Velocity of swimmer = 4 km/hr

Angle = 120°

We need to draw a figure,

Here, $V_{s}$ is the velocity of swimmer w.r.to river, $V_{r}$ is the velocity of river w.r. to ground and V is the velocity of swimmer w.r.to ground.

$tan 90=\dfrac{V_{s}\sin\theta}{V_{r}+V_{s}\cos\theta}$

$\dfrac{\sin 90^{\circ}}{\cos90^{\circ}}=\dfrac{V_{s}\sin120^{\circ}}{V_{r}+V_{s}\cos120^{\circ}}$

$V_{r}+V_{s}\cos120^{\circ}=0$

$V_{r}=-V_{s}\cos120^{\circ}$

Put the value in equation (I)

$V_{r}=-4\times(-\dfrac{1}{2})$

$V_{r}=2 km/hr$

Hence, The speed of the river is 2 km/hr.