Question

A swimmer can swim in still water with speed v and the river is flowing with velocity v/2. To cross the river in shortest distance, he should swim making angle θ with upstream. What is the time taken to swim across the shortest distance ?

Answer 1

Let distance = d, angle made with the upstream = theta

Therefore, 90- theta = angle made with the normal stream Therefore time taken = t’ = d/v cos (90-theta) = d/v sin theta Also t = d/v

Therefore, required ratio = t/t’= (d/v)/ (d/v sin theta) = sin theta

Answer 2

Answer:

sin theta

Explanation:

Let distance = d, angle made with the upstream = theta

Therefore, 90- theta = angle made with the normal stream

Therefore time taken = t’ = d/v cos (90-theta) = d/v sin theta Also t = d/v

Therefore, required ratio = t/t’= (d/v)/ (d/v sin theta) = sin theta