Motion in a Plane · Question 16

A river is flowing from west to east direction with speed of 9 km h-1. If a boat capable of moving at a maximum speed of 27 km h-1 in still water, crosses the river in half a minute, while moving with maximum speed at an angle of 150 to direction of river flow, then the width of the river is :

1. 112.5 m
2. 75 m
3. 300 m
4. 112.5 3 m

Answer

(1) 112.5 m

Solution

Only the component of the boat's velocity (relative to water) across the river carries it to the other bank; the river flow is along the bank.

v = 27 150 = 27 12 = 13.5 km h-1

= 13.5 518 = 3.75 m s-1

Time t = 30 s

Width = v t = 3.75 30 = 112.5 m

Answer: (1)