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Q3E

Expert-verifiedFound in: Page 121

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

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

The east component is 3.8 km

The north component is 3.2 km

**A vector is a quantity that has both magnitude and direction. Displacement, velocity, force, torque, and other vector quantities are some examples of vector quantities.**

In triangle ABC:

$\begin{array}{rcl}\angle ABC& =& {90}^{\xb0}-{40}^{\xb0}\\ & =& {50}^{\xb0}\end{array}$

$\mathrm{BC}=5\mathrm{km}$

AC = Base

BC = Hypotenuse

AB = Perpendicular

For the north component, in the right-angled triangle:

$\begin{array}{rcl}\mathrm{cos}\theta & =& \frac{base}{hypotenous}\\ \mathrm{cos}{50}^{\xb0}& =& \frac{base}{5}\\ 0.64& =& \frac{base}{5}\\ base& =& 3.2km\end{array}$

Therefore, towards the north component, the displacement of the hiker is 3.2 km.

For the east component, in a right-angled triangle:

$\begin{array}{rcl}\mathrm{sin}\theta & =& \frac{Perpendicular}{hypotenous}\\ \mathrm{sin}{50}^{\xb0}& =& \frac{perpendicular}{5}\\ 0.77& =& \frac{perpendicular}{5}\\ Perpendicular& =& 0.77\times 5\\ perpendicular& =& 3.8km\end{array}$

Therefore, towards the east component, the displacement of the hiker is 3.8 km.

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