Question

On an open ground a motorist follows a track that turns to his left by an angle of 60 degree after every 500m. starting from a given turn, specify the displacement of the motorist at the third, sixth and the eight turn. compare the magnitude of displacement with the total path length covered by the motorist in each case.

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Answer 1

QUESTION⤵️

On an open ground a motorist follows a track that turns to his left by an angle of 60 degree after every 500m. starting from a given turn, specify the displacement of the motorist and the third, sixth and eighth turn. compare the magnitude of displacement with the total path length covered by the motorist in each case.

ANSWER⤵

At III turn➡️

|Displacement|. = |OA + AB + BC| = |OC|

=500 cos 60° + 500+ 500 cos 60°

= 500×1/2 + 500+ 500 × 1/2

= 1000m

so |Displacement|= 1000m from O to C

Distance = 500+50+500

= 1500m

therefore, displacement/ distance= 1000/1500= 2/3

At IV turn➡

as initial and final positions are same so displacement = 0

and distance= 500× 6= 3000m

therefore, displacement/distance=0/3000=0

At VIII turn➡

|Displacement|= 2(500) cos(60°/2) = 1000×cos 30° = 1000× ✓3/2

=500✓3m

Distance= 500×8= 4000m

therefore, Displacement/distance= 500✓3/4000=✓3/8

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