A man crosses a river in a boat. If he crosses the river in minimum time, he takes 10 min with a drift 120 m . If he crosses the river taking the shortest path, he takes 12 . 5 min , find the width of the river.

Step-by-step solution

Let v r = velocity of river v br = velocity of river in still water and w = width of river Given,   t min   =   10   min or w v br = 1 0 ...(i) Drift, in this case, will be, x = v r t ∴ 120 = 10 v r ...(ii) The shortest path is taken when v b is along AB . In this case, v b = v br 2 - v r 2 Now, 1 2 . 5 = w v b = w v br 2 - v r 2 ...(iii) Solving these three equations, we get v br   =   20   m   min - 1 , v r   =   12   m   min - 1 and w =   200