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Q15PE

Expert-verified
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.