May 6th, 2009, 02:35 PM  #1 
Member Joined: May 2009 Posts: 58 Thanks: 0  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 = rh : r 1:3 = rh : r r=3r3h 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) 
May 6th, 2009, 02:37 PM  #2 
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