Question

Ship $A$ is travelling with a velocity of $5{\text{km h}}^{-1}$ due east. The second ship is heading ${30}^{\circ }$ east of north. The speed of second ship if it is to remain always due north with respect to the first ship in ${\text{km h}}^{-1}$ is

Answer 1

For $B$ always to be north of $A$, the velocity components of both along east should be same.
$v_2\cos {60}^{\circ }=v_1$
$\Rightarrow v_2=\frac{v_1}{cos{60}^{\circ }}$
$\Rightarrow v_2=2\times v_1$
$\Rightarrow v_2=10km/h$