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May 6th, 2009, 02:35 PM   #1
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Related rates

1. A man 6 ft tall walks at rate of 200 feet per minute towards a street light which is 18 ft above the ground. At what rate is the tip of his shadow moving?
Answer :
let shadow of street light = h and dh/dt = rate of change in street light shadow
let shadow of man to the street light= r and rate of change of the tip of his shadow = dr/dt

The man and the street light form two similar triangles which gives:
height of street light : height of man = shadow of street light : shadow of man
6 : 18 = r-h : r
1:3 = r-h : r
r=3r-3h
2r=3h
differentiate each with respect to time t
2dr/dt = 3dh/t
2dr/dt = 3 (-200)
dr/dt = -300 ft/minute (I'm not sure whether it should be -300 or +300)
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May 6th, 2009, 02:37 PM   #2
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Re: Related rates

This was answered previously:

viewtopic.php?f=15&t=7826
 
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