A swimmer desires to cross a 500 m wide river that is flowing at 5 km/h . His speed relative to the water is 3 km/h . If he heads in a direction making an angle with the flow, determine the time he takes to cross the river.

Step-by-step solution

Width of the river, d = 500 m = 0.5 km Velocity of the swimmer relative to water, v_ sr = 3 km/h Angle made by the swimmer with the direction of river flow = Component of the swimmer's velocity perpendicular to the river flow = v_ sr = 3 km/h Time taken to cross the river, t = d v_ sr t = 0.5 3 hours t = 0.5 60 3 minutes = 10 minutes