A person moves 30, m north and then 20, m tow | vedclass

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(C) Let the origin be $O(0, 0)$.$1$. The person moves $30\, m$ north: $\vec{OA} = 30\hat{j}$.$2$. Then moves $20\, m$ east: $\vec{AB} = 20\hat{i}$.$3$

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$10\, m$ along west

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(C) Let the origin be $O(0, 0)$.$1$. The person moves $30\, m$ north: $\vec{OA} = 30\hat{j}$.$2$. Then moves $20\, m$ east: $\vec{AB} = 20\hat{i}$.$3$. Finally moves $30\sqrt{2}\, m$ in south-west direction (at $45^\circ$ to both south and west): $\vec{BC} = 30\sqrt{2} \cdot (-\cos 45^\circ \hat{i} - \sin 45^\circ \hat{j}) = 30\sqrt{2} \cdot (-\frac{1}{\sqrt{2}} \hat{i} - \frac{1}{\sqrt{2}} \hat{j}) = -30\hat{i} - 30\hat{j}$.Net displacement $\vec{OC} = \vec{OA} + \vec{AB} + \vec{BC} = (0\hat{i} + 30\hat{j}) + (20\hat{i} + 0\hat{j}) + (-30\hat{i} - 30\hat{j}) = -10\hat{i} + 0\hat{j}$.The magnitude is $|\vec{OC}| = 10\, m$ and the direction is along the negative x-axis,which is west.

$A$ 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

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