College Physics 3.3 – North and East components of a displacement


Find the north and east components of the displacement for the hikers shown in Figure 3.50.

A displacement S is shown with magnitude of 5.0 km and directed 40 degrees north of east.
Figure 3.50

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.

A displacement vector S with magnitude of 5.0 km and directed at 40° north of east. Also shows the east and west component of the vector using the parallelogram law.

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}