A swimmer crosses a river along a line making 45° with the direction of flow. River speed is 5 m s⁻¹. The river is 60 m wide and the swimmer takes 6 s to cross. The swimmer's speed relative to water is:
Options

Question

A swimmer crosses a river along a line making 45° with the direction of flow. River speed is 5 m s⁻¹. The river is 60 m wide and the swimmer takes 6 s to cross. The swimmer's speed relative to water is:

Options

G1 Physics · Accepted Answer

The river is 60 m wide and crossing time is 6 s, so the ground velocity component across the river is 10 m s⁻¹. The actual path makes 45° with river flow, so ground downstream component is also 10 m s⁻¹. Current contributes 5 m s⁻¹ downstream, hence swimmer-relative-water components are 10 m s⁻¹ across and 5 m s⁻¹ downstream. Speed=√(10²+5²)=5√5 m s⁻¹. Hence option C.