Question

From the shore ,Navy patrol boat travels 45 degree south of east for 60 km and then turns 60 degree south of west for another 36 km before reaching a sinking ship.Give the shortest route ( magnitude and direction) that the boat could have taken to reach the sinking ship?

Answer 1

$s_x=s_{x1}+s_{x2}=60\cdot\cos60°-36\cdot\cos60°=12(km)$

$s_y=s_{y1}+s_{y2}=60\cdot\sin60°+36\cdot\sin60°=83.14(km)$

So,

$s=\sqrt{12^2+83.14^2}=84(km)$

$\alpha=\arctan(\frac{s_y}{s_x})=\arctan(\frac{83.14}{12})=81.8°$