First slide

Scalars and 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, $\vec{O A} = 0 \hat{i} + 30 \hat{j}, \vec{A B} = 20 \hat{i} + 0 \hat{j}$
$\begin{array}{l} \vec{B C} = - 30 \sqrt{2} \cos 45^{\circ} \hat{i} - 30 \sqrt{2} \sin 45^{\circ} \hat{j} = - 30 \hat{i} - 30 \hat{j} \\ ∴ Net displacement, \vec{O C} = \vec{O A} + \vec{A B} + \vec{B C} = - 10 \hat{i} + 0 \hat{j} \\ \Rightarrow | \vec{O C} | = 10 m \end{array}$ Net displacement is 10m along west

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