Question

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 water. Assume $V_B=2V_W.$ What is the time taken by the boat, if boat has to cross the river directly on the AB line? ($D=$ width of river)

• A. $\frac{2D}{V_B\sqrt{3}}$
• B. $\frac{\sqrt{3}D}{2V_B}$
• C. $\frac{D}{V_B\sqrt{2}}$
• D. $\frac{D\sqrt{2}}{V_B}$

Answer 1

The correct option is A $\frac{2D}{V_B\sqrt{3}}$

To move straight along AB,
$v\sin \theta =V_W\sin \theta =\frac{V_W}{V_B}=\frac{V_W}{2V_W}=\frac{1}{2}\therefore \theta ={30}^{\circ }$

Time taken to cross the river,
$t=\frac{D}{V_{B}cos\theta }=\frac{D}{V_{B}cos{30}^{\circ }}=\frac{2D}{V_B\sqrt{3}}$