Question

A bus moves 15 km east and turns 45 ᵒ N of E for another 5 km before coming to stop. Find the magnitude and direction of the resultant displacement of the bus.

Answer 1

$$d_x=15+5\cos 45^\circ=18.5\:{\rm km}\\ d_y=0+5\sin 45^\circ=3.54\:\rm km$$

$$d=\sqrt{18.5^2+3.54^2}=16\:\rm km$$

$$\theta=\tan^{-1}\frac{3.54}{18.5}=11^\circ\;\rm N\:of\: E$$