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Found in: Page 122

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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

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

See the step by step solution

## Step 1: 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.

## Step 2: Determining north component

The north component of displacement from San Francisco to Sacramento is

${s}_{n}=S\mathrm{sin}\left(45°\right)$

Here S is the magnitude of the displacement.

Substitute 123 km for S.

${s}_{n}=123km×\mathrm{sin}45°\phantom{\rule{0ex}{0ex}}=86.97km$

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

## Step 3: Determining east component

The east component of displacement from San Francisco to Sacramento is

${s}_{E}=S\mathrm{cos}\left(45°\right)\phantom{\rule{0ex}{0ex}}$

Here S is the magnitude of the displacement.

Substitute 123km for S .

${S}_{E}=123km×\mathrm{cos}\left(45°\right)\phantom{\rule{0ex}{0ex}}=86.97km$

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