Question

A man starts from $O$ moves $500m$ turns by ${60}^{\circ }$ and moves $500m$ again turns by ${60}^{\circ }$ and moves $500m$ and so on. Find the displacement after $\left(i\right)$ 5th turn , $\left(ii\right)$ 3rd turn.

• A. -$500m,1000m$
• B. $500m,500\sqrt{3}m$
• C. $1000m,500\sqrt{3}m$
• D. none of these

Answer 1

The correct option is A -$500m,1000m$

(i) Fifth turn is at E and this displacement will be given by vector $\overrightarrow{OE}$ which is clear from the given fig that it is- $500m$.

(ii) Third turn is at C and this will be given by vector $\overrightarrow{OC}$ which is equal to $\sqrt{A{C}^2+A{B}^2}=\sqrt{(500\sqrt{3}{)}^2+{500}^2}=1000m$ where $AC=2ABsin{60}^o$