Question

Find the north and east components of the displacement from San Francisco to Sacramento shown in Figure 3.57.

Short answer

The north component of the displacement vector is$86.97m$, and the east component of the displacement vector is $86.97m$.

Step-by-step solution

Defining vector

A vector is a physical quantity that has both magnitude and direction. The vector can be split into two or more scalar components when added, producing the same effect as it produced by a single vector.

Determining north component

The north component of displacement from San Francisco to Sacramento is

$s_n=S\sin (45°)$

Here S is the magnitude of the displacement.

Substitute 123 km for S.

$$\begin{gathered} s_n=123km\times \sin 45° \\ =86.97km \end{gathered}$$

Hence, the north component of the displacement from San Francisco to Sacramento is 86.97km.

Determining east component

The east component of displacement from San Francisco to Sacramento is

$s_E=S\cos (45°)$

Here S is the magnitude of the displacement.

Substitute 123km for S .

$$\begin{gathered} S_E=123km\times \cos (45°) \\ =86.97km \end{gathered}$$

Hence, the east component of the displacement from San Francisco to Sacramento is 86.97km.