Question

.
is
A swimmer reaches the other bank of a flowing
river exactly opposite to the starting point. If he was
swimming at 2 km/hr while maintaining 150° with
the flow, then time taken by him to cross the river
1 km wide is
h
e
(1) 30 min
(2) 1 hr
1
(3) 2 hrs
(4) 20 min
​​

Answer 1

Answer:

1 hour

Explanation:

given v = 2km/hr

also, given that the swimmer's final point is directly opposite to his initial point. So, the swimmer swimmed in a straight line.

=> there is no displacement in horizontal direction, thats why the swimmer reached the point directly opposite to him.

hence, the horizontal component of the swimmers velocity cancelled out the velocity of the flow of the river.

hence, the swimmer's horizontal component is used up to cancel out the flow of the river.

=> the swimmer crossed the 1km wide river with his vertical component of his velocity.

given, he maintains 150° with the flow. So the angle he makes with the horizontal is 30° ( 180 - 150).

hence his vertical component of velocity = vsin30 = 2km/hr × sin 30 = 2 × 1/2 = 1km/hr.

hence, vertical component of his velocity is 1km/hr.

=> distance = width of river = 1km

speed = vertical component = 1km/hr

hence time = distance/speed = 1/1 = 1hr

hence, the swimmer crosses the river in 1hour