Question

Albert is going for a walk follows the path 300m East, then he going to 100m South, after a rest he proceed to 200m,30⁰South of West and lastly, he continues to 150m, 60⁰ North of West and stop. The total trip consists of four straight-line paths. At the end of the walk, what is the person’s resultant displacement measured from the starting point?

Answer 1

Let's find $x$ and $y$ components of the resultant displacement:

$d_x=300\ m\cdot cos0^{\circ}+100\ m\cdot cos270^{\circ}+200\ m\cdot cos(180^{\circ}+30^{\circ})+150\ m\cdot cos(180^{\circ}-60^{\circ})=51.8\ m,$$d_y=d_x=300\ m\cdot sin0^{\circ}+100\ m\cdot sin270^{\circ}+200\ m\cdot sin(180^{\circ}+30^{\circ})+150\ m\cdot sin(180^{\circ}-60^{\circ})=-70.1\ m.$Then, the resultant displacement can be found from the Pythagorean theorem:

$$d=\sqrt{d_x^2+d_y^2}=\sqrt{(51.8\ m)^2+(-70.1\ m)^2}=87.16\ m.$$

We can find the angle as follows:

$$\theta=sin^{-1}(\dfrac{d_y}{d})=sin^{-1}(\dfrac{-70.1\ m}{87.16\ m})=-53.5^{\circ}.$$

The sign minus means that resultant displacement has direction $53.5^{\circ} S\ of\ E$.

Therefore, the resultant displacement $d$ has magnitude 87.16 m and direction of $53.5^{\circ} S\ of\ E$.