First slide

Vectors

Question

A person moves 30 m north and then 20 m towards east and finally $30 \sqrt{2} m$ in south-west direction. The displacement of the person from the origin will be

Moderate

A

10 m along north
B

10 m long south
C

10 m along west
D

zero

Solution

From figure, $\vec{OA} = 0 \hat{i} + 30 \hat{j}, \vec{AB} = 20 \hat{i} + 0 \hat{j}$
$\vec{BC} = - 30 \sqrt{2} \cos 45^{0} \hat{i} - 30 \sqrt{2} \sin 45^{0} \hat{j}$
= $- 30 \hat{i} - 30 \hat{j}$
$∴$ Net displacement, $\vec{OC} = \vec{OA} + \vec{AB} + \vec{BC}$
= $- 10 \hat{i} + 0 \hat{j}$
= $| \vec{OC} | = 10 m .$

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