Question

A man wishes to cross a river in a Boat if he crosses the river in minimum time it takes 10 minutes with a drift of 120 m. if he crosses the river taking shortest route he takes 12.5 minutes find the velocity of boat .

Answer 1

velocity of river = 120m/10min = 12m/min now for the man in second case (shortest path) vx² + vy² = v² where v is magnitude of man's velocity

but we have, vy =12m/min since its the shortest path

so vx = √(v² -12² )

for the shortest time
distance d= time *velocity = 10v

for the shortest path distance
d= 12.5*√(v² -12² )

therefore, 10v=12.5*√(v² -12² )
10² v² = (12.5)² (v² -12² )
v² (12.5²- 10²)= (12.5)² *12²

v= root (12.5)² *12²) /(12.5²- 10²)
v=12*12.5/56.25

v= 2.66 m/sec Ans.