Question

The displacement vector from your house to the library is 760 m long, pointing 35° north of east. What are the components of this displacement
vector?

Answer 1

Answer:

The two components of displacement vector are:

$East:760\cos 35=622.56\ m\\North:760\sin 35=435.92\ m$

Explanation:

Given:

The magnitude of displacement is 760 m.

The direction of the displacement vector is 35° North of East.

North of East means that the vector is between North and East and makes an angle of 35° with the east direction.

Now, there are two components of this displacement vector. One component is along the East direction and the other perpendicular to the East direction which is the North direction.

Component along the East direction is given as:

$East:760\cos 35=622.56\ m$

Component along the North direction is given as:

$North:760\sin 35=435.92\ m$

Therefore, the two components that are mutually perpendicular to each other are 622.56 m East and 435.92 m North.