Q 11-03-113JEE MainJEE Main 2022 (25 Jul, Shift 1)Medium
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 $\cos135^\circ = -0.7$)
Answer: (B) $47\ \text{m}$
Arc length: $R\theta = 60$ with $\theta = \dfrac{3\pi}{4}$, so $R = \dfrac{240}{3\pi}\approx25.5\ \text{m}$.
Displacement (chord $AB$):
$$AB = \sqrt{R^2 + R^2 - 2R^2\cos135^\circ} = R\sqrt{2(1 + 0.7)} = 25.5\times1.84\approx47\ \text{m}$$
Solution by Sreeraj P, M.Sc Physics