Answer to Question #269865 in Physics for Joey

Question

Find the resultant vector using component method:

A = 20km, Eastward

B= 15km, 35 degrees North of West

Answer 1

The components:

$$A_E=20\text{ km},\\ A_N=0.\\ B_E=-15\cos35°=-12.3\text{ km},\\ B_N=15\sin35°=8.6\text{ km}.$$

The resultant is

$$|r|=\sqrt{(A_E+B_E)^2+(A_N+B_N)^2}=11.54\text{ km},\\\space\\ \theta=\arctan\frac{A_N+B_N}{A_E+B_E}=48.16°\text{ N of E}.$$