A swimmer wishes to cross a 500 m wide river flowing at 5 km/h. His speed with respect to water is 3 km/h. (a) If he heads in a direction making an angle θ with the flow, find the time he takes to cross the river. (b) Find the shortest possible time to cross the river.
Given:
Width of the river = 500 m
Rate of flow of the river = 5 km/h
Swimmer’s speed with respect to water = 3 km/h
As per the question, the swimmer heads in a direction making an angle θ with the flow.
We know that the vertical component of velocity 3sinθ takes him to the opposite side of the river.
Distance to be travelled = 0.5 km
Vertical component of velocity = 3sinθ km/h
(a)Thus, we have:
(b) Shortest possible time to cover the river:
Taking, 
Hence, the required time is 10 minutes.