Question

A hicker begins a trip by first walking 25 km south east from her car then she walks 40 km in a direction 60 degree centigrade north of East (a) determine the component for each displacement (b) determine R esultant displacement

Answer 1

a)

$$d_{1x}=25\cos{45}=17.68\ km$$

$$d_{1y}=-25\sin{45}=-17.68\ km$$

$$d_{2x}=40\cos{60}=20\ km$$

$$d_{2y}=40\sin{60}=34.64\ km$$

b)

$$R_x=17.68+20=37.68\ km$$

$$R_y=-17.68+34.64=16.96\ km$$

The magnitude:

$$R=\sqrt{37.68^2+16.96^2}=41.3\ km$$

The direction:

$$\theta=\arctan{\frac{16.96}{37.68}}=24.2\degree N\ of\ E$$