Question

A person travels following displacement:
3m North
4m West
5m south to east 45 degree
Find its resultant displacement if sin45=cos45=0.7

Answer 1

Let the y-axis is directed toward North and x-axis toward West. Then

$$S_x=S_{1x}+S_{2x}+S_{3x}$$

$$S_x=0+4-5\cos 45^{\circ}=0.5\:\rm{m}$$

$$S_y=S_{1y}+S_{2y}+S_{3y}$$

$$S_y=3+0-5\sin 45^{\circ}=-0.5\:\rm{m}$$

The magnitude of resultant displaement

$$S=\sqrt{S_x^2+S_y^2}=\sqrt{0.5^2+(-0.5)^2}=0.7\:\rm{m}$$

Direction

$$\theta=\tan^{-1}\frac{S_y}{S_x}=\tan^{-1}\frac{-0.5}{0.5}=-45^{\circ}$$

(45 degree South of West)