Q. A boat crosses a river from port $A$ to port $B$, which are just on the opposite side. The speed of the water is $V_{W}$ and that of boat is $V_{B}$ relative to still water. Assume $V_{B} = 2V_{W}$. What is the time taken by the boat, if It has to cross the river directly on the $AB$ line
A) $\frac{2D}{V_{B}\sqrt{3}}$
B) $\frac{\sqrt{3}D}{2V_{B}}$
C) $\frac{D}{V_{B}\sqrt{2}}$
D) $\frac{D\sqrt{2}}{V_{B}}$
Explanation
(a) [image:3_image207.emf]
From figure, $V_{B}\sin\theta = V_{W}$
$\sin\theta = \frac{V_{W}}{V_{B}} = \frac{1}{2} \Rightarrow \theta = 30{^\circ}\ \ \ \ \ \ \ \lbrack\because V_{B} = 2V_{W}\rbrack$
Time taken to cross the river,
$t = \frac{D}{V_{B}\cos\theta} = \frac{D}{V_{B}\cos{30{^\circ}}} = \frac{2D}{V_{B}\sqrt{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.