Question

An ambulance has successive displacements of 6.3km, 45 deg., 12km south; and 4.7 km, 30 deg. south of west. a] Determine the magnitude and directionof the resultant displacement b].What is the total distance traveled by the ambulance?

Answer 1

a)

$$s_x=6.3\cos{45}+4.7\cos{30}=8.5\ km\\s_y=6.3\sin{45}+12+4.7\sin{30}=18.8\ km$$

$$s=\sqrt{8.5^2+18.8^2}=20.6\ km$$

$$\theta=\arctan{\frac{8.5}{18.8}}=24\degree \text{ W of S}$$

b)

$$d=6.3+12+4.7=23\ km$$