# College Physics 3.3 – North and East components of a displacement

## Solution:

To solve for the north and east components of the given displacement vector, we need to draw them first by virtue of the parallelogram law. The vector, together with its components, is shown in the figure below.

We can solve the north and east components by considering the right triangle ABC. The east component is the side AC and the north component is the side BC.

The North-component is given by

$\displaystyle \text{s}_{\text{north}}=\left(5.0\:\text{km}\right)\text{sin}\:\left(40.0\right)^{\circ}$

$\text{s}_{\text{north}}=3.21\:\text{km}$

The East-component is given by

$\displaystyle \text{s}_{\text{east}}=\left(5.0\:\text{km}\right)\text{cos}\left(40.0\right)^{\circ}$

$\text{s}_{\text{east}}=3.83\:\text{km}$