Answer to Question #136433 in Physics for Matilda Salaum

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,

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

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