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

• A. 10 m along north
• B. 10 m long south
• C. 10 m along west
• D. Zero

Answer 1

Answer: (C)

10 m along west

Answer 2

From figure, $\overset{\rightarrow}{OA} = 0\mspace{6mu}\overset{\rightarrow}{i} + 30\mspace{6mu}\overset{\rightarrow}{j}$, $\overset{\rightarrow}{AB} = 20\mspace{6mu}\overset{\rightarrow}{i} + 0\mspace{6mu}\overset{\rightarrow}{j}$

$\overset{\rightarrow}{BC} = - 30\sqrt{2}\mspace{6mu} cos45^{o}\overset{\rightarrow}{i} - 30\sqrt{2}\mspace{6mu}\sin 45^{o}\overset{\rightarrow}{j}$ $= - 30\mspace{6mu}\overset{\rightarrow}{i} - 30\mspace{6mu}\overset{\rightarrow}{j}$

∴ Net displacement, $\overset{\rightarrow}{OC} = \overset{\rightarrow}{OA} + \overset{\rightarrow}{AB} + \overset{\rightarrow}{BC} = - 10\mspace{6mu}\overset{\rightarrow}{i} + 0\mspace{6mu}\overset{\rightarrow}{j}$

$|\overset{\rightarrow}{OC}|\mspace{6mu} = 10\mspace{6mu} m.$