Question

A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be : (Given cos135° = - 0.7)

(A) 42 m

(B) 47 m

(C) 19 m

(D) 40 m

Answer 1

Correct option is (B) 47 m

Distance travelled = 60 m

⇒ Angle covered = 135^∘

Displacement AB = \(\sqrt{R^2 + R^2 - 2R^2\cos 135° }\)

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

\(= 2(\frac{80}\pi) (0.85)^{1/2}\)

\(\approx 47\) m

Answer 2

Correct option is (B) 47 m