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)

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47 m

19 m

40 m

42 m

answer is B.

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Detailed Solution

$\begin{array}{l} d = Rθ \\ 60 = R (\frac{3 π}{4}) \\ R = \frac{60 \times 4}{3 π} = \frac{80}{π} m \\ Displacement = \sqrt{R^{2} + R^{2} - 2 R^{2} \cos 135} \\ \Rightarrow \sqrt{2 R^{2} - 2 R^{2} (- 0 .7)} \\ \Rightarrow \sqrt{3 .4 R^{2}} = \sqrt{3 .4 {(\frac{80}{π})}^{2}} \\ \approx 47 m \end{array}$

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