If a boy moving on a motor cycle in a ground takes a turn through on his left after every 50m. then choose the correct from the following

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the magnitude of distance suffered by him after 9^th turn is 450 m

the magnitude of displacement suffered by him after 9^th turn is 50 m

the magnitude of distance suffered by him after 9^th turn is 400 m

the magnitude of displacement suffered by him after 9^th turn is 100 m

answer is A, C.

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Detailed Solution

$\vec{O B} = \vec{O A} + \vec{A B}$

$∴ O B = 2. O A . \cos (\frac{60}{2}) = 50 \sqrt{3} m$

$\vec{O B} + \vec{B C} = \vec{O C}$

$∴ O C = \sqrt{O B^{2} + B C^{2}} = 100 m$

$∴$ The magnitude of displacement after 9^th turn = 100 m and distance = 450 m .

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