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A person moved from A to B on a circular path as shown is fig.
If the distance travelled by him is 90m, then the magnitude of displacement would be (Given $c o s 135^{0} = - 0.7)$

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42.26 m

70.46 m

19.37 m

40.87 m

answer is B.

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Detailed Solution

$d=Rθ$

$90 =R (\frac{3π}{4})$

$R= \frac{90×4}{3π} = \frac{120}{π}$

$∴$ Displacement $= \sqrt{R^{2} + R^{2} - 2 R^{2} \cos 135^{0}} = \sqrt{{3.4R}^{2}} = \sqrt{3.4 {(\frac{120}{π})}^{2}} \approx 70.46m$

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