Question

A man travels 7.0km due North,then 10.0km East,find the resultant displacement.If he travels 7.0km 30degrees East of North,then 10.0km East,find the resultant displacement

Answer 1

1)

$$d=\sqrt{7^2+10^2}=12.2\ km$$

$$\theta=\arctan{\frac{7}{10}}=35\degree \ North\ of \ East$$

2)

$$d=\sqrt{7^2+10^2+2(7)(10)\cos{(90-30)}}=14.8\ km$$

$$\theta=\arctan{\frac{7\cos{30}}{10+7\sin{30}}}=24.2\degree \ North\ of \ East$$