Ques. 1JEE Main 2025, 2 April (Morning Shift)
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 :
- 112.5 m
- 75 m
- 300 m
- 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)