Question

A boat crosses a river from port $A$ to port $B$, which are directly opposite to each other. The speed of the water is $v_w$ and that of boat is $V_b$ relative to water. Assume $V_b=2V_w$. The time taken by the boat, if it has to cross the river directly on the $AB$ line is $(\text{given}AB=D)$

• 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 $\frac{2D}{V_b\sqrt{3}}$


For the boat to travel along $AB$, the net velocity in horizontal direction should be zero.
$\Rightarrow V_x=0-V_b\sin \theta +V_w=0\Rightarrow -2V_w\sin \theta =-V_w(\because V_b=2V_w)\Rightarrow \theta ={30}^{\circ }\text{Time}=\frac{D}{V_b\cos {30}^{\circ }}=\frac{2D}{V_b\surd 3}$