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A ship A travels in the north making an angle of 45? to the West with a velocity of 18 km/hr and ship B travels in the East with a velocity of 9 km/hr. Find the relative velocity of B w.r.t. ship A.
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$\begin{align*}V_A&=18kmph \nwarrow \\[2ex] &=5m/s\angle 135^\circ\\[2ex] &=5\cos 135i+5\sin 135j\\[2ex] &=-3.54i+3.54jm/s\end{align*}$

$\begin{align*}V_B&=9kmph \rightarrow \\[2ex] &=2.5m/s\rightarrow \\[2ex] &=2.5im/s\end{align*}$

$\begin{align*}\overline V_{A/B}&=\bar V_B-\bar V_A\\[2ex] &=2.5i-(-3.54i+3.54j)\\[2ex] &=6i-3.54j\\[2ex] &=7m/s\searrow 31^\circ\end{align*}$

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