Question

A cyclist moves in such a way that he takes ${72}^{\circ }$ turn towards left after travelling 200 m in straight line. What is the displacement when he takes just takes fourth turn?

• A. Zero
• B. 600 m
• C. 400 m
• D. 200 m

Answer 1

The correct option is D 200 m

$\overrightarrow{s_1}=200i\overrightarrow{s_2}=200(\cos {72}^{o}i+\sin {72}^{o}j)\overrightarrow{s_3}=200(\cos {144}^{o}i+\sin {144}^{o}j)\overrightarrow{s_4}=200(\cos {216}^{o}i+\sin {216}^{o}j)\therefore \overrightarrow{s_{net}}=\overrightarrow{s_1}+\overrightarrow{s_2}+\overrightarrow{s_3}+\overrightarrow{s_4}=200(1+\cos {72}^o+\cos {144}^o+\cos {216}^o)\hat{i}+200(\sin {72}^o+\sin {144}^o+\sin {216}^o)\hat{j}=200(-0.309)\hat{i}+200\left(0.95\right)\hat{j}\Rightarrow \left|\overrightarrow{s_{net}}\right|=200m$