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. What should be the speed of second ship if it is to always remain due north with respect to the first ship?

• A. $10{\text{km h}}^{-1}$
• B. $9{\text{km h}}^{-1}$
• C. $8{\text{km h}}^{-1}$
• D. $7{\text{km h}}^{-1}$

Answer 1

The correct option is A $10{\text{km h}}^{-1}$

For $B$ always to be north of $A$, the velocity components of both along east should be same.
Therefore,
$v_2\cos {60}^{\circ }=v_1\Rightarrow v_2=10{\text{km h}}^{-1}$