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June 23rd, 2012, 03:29 PM   #1
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Related Rate Problem

I keep getting the height to be 143 cm using similar triangles and differentiating.

I am reading up on latex now to type up my steps.
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June 23rd, 2012, 04:07 PM   #2
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Re: Related Rate Problem

A spotlight on the ground shines on a wall 1,000 cm away. A boy walks from the spotlight toward the wall at a speed of 120 cm/sec. At the moment when the boy is 400 cm from the wall, the length of his shadow on the wall is decreasing at 46 cm/sec. How tall is the boy?
Comparing the triangles, you get the following proportion:
the height of the boy : his distance from the spotlight :: the height of his shadow : the distance from the wall to the spotlight

Letting h be the height of the boy, x be his distance from the spotlight, and s be the height of his shadow, h/x = s/1000.
Hence .

Substitute ds/dt = -46, dx/dt = 120, and x = 600, then solve for h.
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June 23rd, 2012, 04:46 PM   #3
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Re: Related Rate Problem

thanks man my mistake was not treating 1000h like a constant which it is since it does not depend on time.

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