May 4th, 2009, 03:08 AM  #1 
Member Joined: May 2009 Posts: 58 Thanks: 0  Related rates
Please help me to check the solutions. Thanks for your help 1. a particle moves along a path described by y=x^2. at what point along the curve are x and y changing at the same rate? Find this rate if at that time t we have x=sin(t) and y= (sin(t))^2 Answer : dy/dx = 2x = 1 => x = 1/2 and y = 1/4 Point is (1/2, 1/4). dy/dt = 2sint cost and dx/dt = cost dy/dt = dx/dt => 2sint cost = cost => sint = 1/2 => t = ?/6 => rate is cost = cos(?/6) = ?3/2. 2. 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 4th, 2009, 03:31 PM  #2 
Guest Joined: Posts: n/a Thanks:  Re: Related rates
#2: Using similar triangles. Let x=distance between man and pole and y=length of his shadow. Solving for y: We are told dx/dt=200 

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