1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# A boat which has a speed 5 km/h in still water crosses a river 100 m wide along the shortest possible path in 1.5 minutes, the velocity of river water in km/h is

A
3.0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
3.00
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The shortest path that the boat could cross is OB. For this, the boat will have to move against the direction of flow of river at some angle. Assuming origin at point O, rightward direction be positive x− axis and OB be positive y− axis. Let velocity of the river be, →vr=v^i and velocity of boat w.r.t. the ground be →vb. Given that velocity of the boat w.r.t. river, ∣∣→vbr∣∣=5 km/h Now, width of the river, OB=100 m=0.1 km Time taken by the boat to cross the river, t=1.5 min=1.560 h ∴∣∣→vb∣∣=OBt=0.1 km1.560h=6015=4 km/h ⇒→vb=4^j km/h Velocity of boat w.r.t. river, −→vbr=→vb−→vr →vbr=4^j−v^i ∣∣→vbr∣∣=5=√42+v2 v=√25−16=3 km/h ∴ Velocity of river =3 km/h

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos