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 cos 135 ° = - 0 . 7 )

Step-by-step solution

The distance travelled by the person d will be equal to the arch length. ⇒ d = R θ ⇒ 60 = R 3 π 4 ⇒ R = 60 × 4 3 π = 80 π m Now the magnitude of displacement can be found using subtraction of vectors. Therefore, s = R 2 2 + R 1 2 - 2 R 1 R 2 cos θ ⇒ s = R 2 + R 2 - 2 R 2 cos 135 ° ⇒ 2 R 2 - 2 R 2 - 0 . 7 ⇒ 3 . 4 R 2 = 3 . 4 80 π 2 ⇒ R = 47   m