Question

A biker travels 400m E then turns 300m S before going 200m W then 250m NW. What is the resultant vector using the component method?

Answer 1

Find the East and North component of each displacement:

$$A_E=400\text{ m},\\ A_N=0\text{ m}.\\ B_E=0\text{ m},\\ B_N=-300\text{ m}.\\ C_E=-200\text{ m},\\ C_N=0\text{ m}.\\ D_E=-250\sin45°=-177\text{ m},\\ D_N=250\sin45°=177\text{ m}.\\\space\\ R_E=A_E+B_E+C_E+D_E=23\text{ m},\\ R_N=A_N+B_N+C_N+D_N=-122\text{ m},\\ R=\sqrt{R_N^2+R_E^2}=124\text{ m},\\\space\\ \theta=\arctan\frac{R_N}{R_E}=-79.3°\text{ from E to N}$$