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A man is running along a circular track has a speed of 10 kmph. A source of light is at the center of the circular track. A wall along the tangent from which he starts. what is the speed of the shadow of the man on the wall when he covers 1/8 th of the track.

A man is running along a circular track has a speed of 10 kmph. A source of light is at the center of the circular track. A wall along the tangent from which he starts. what is the speed of the shadow of the man on the wall when he covers 1/8 th of the track.

Grade:Upto college level

2 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear ANAM


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from the figur when man is at point P shadow will be at point B

tanΘ =x/r

 x =r tanΘ

differentiate

dx/dt = r sec2Θ dΘ/dt

          =r sec2Θ * W      where w is angular velocity

          =v sec2Θ

at 1/8 th of the track it will cover an angel  π/4

so dx/dt = 10* 2 =20 kmph

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Rahul
11 Points
6 years ago
This means when particle move from point A along P..the shadow move along AB...if we assume AP=10..then shadow must travel AB in 1 hr ....then 2*pi*r=80...subtituting r in tan formula we dont get x=20...can u tel me wt wrong i did in this?

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