Looking for classes? Ksquare Career Institute, Bengaluru →
Relative Velocity: River-Boat Problems
Concepts tested here
- Shortest path crossing
All Questions
2000 AIPMT 1 question
-
The width of river is 1 km. The velocity of boat is 5 km/hr. The boat covered the width of river with shortest possible path in 15 min. Then the velocity of river stream is :For the shortest path, the boat is steered upstream at an angle so that its resultant velocity is straight across the river.
Then the speed across the river is $\sqrt{u^2 - v^2}$, where u = 5 km/h is the boat speed in still water and v the river speed.
Time: $t = \dfrac{d}{\sqrt{u^2 - v^2}}$
$\dfrac{1}{4}$ h $= \dfrac{1}{\sqrt{25 - v^2}} \Rightarrow \sqrt{25 - v^2} = 4$
$25 - v^2 = 16 \Rightarrow v = 3$ km/hr