Question

A person moved from $A$ to $B$ on a circular path as shown in figure. If the distance travelled by him is $60\text{m}$, then the magnitude of displacement would be (Given $\cos {135}^{\circ }=–0.7$)

Answer 1

Distance travelled $=60\text{m}$

$\Rightarrow$ Angle covered $={135}^{\circ }$

Displacement $AB=\sqrt{R^2+R^2-2R^2\cos {135}^{\circ }}$

$=2(\frac{60}{135}\times \frac{180}{\pi }){\left[\frac{1-\cos \left({135}^{\circ }\right)}{2}\right]}^{1/2}$

$=2\left(\frac{80}{\pi }\right)(0.85{)}^{1/2}\approx 47\text{m}$

Hence, $\left(B\right)$ is the correct answer.