Andy is 6 feet tall and is walking away from a street light that is 30 feet above ground at a rate of 2 feet per second. How fast is his shadow increasing in length?

1 Answer
Steve M
Nov 2, 2016

# 2.5 # feet/sec

Explanation:

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Let the man be #x# feet away from the street light, and his shadow length be #y#, Let the tip of the shadow be #l# feet away from the light such that #l=x+y# and we are given that #dx/dt=2#

By similar triangles:

# y/6=(x+y)/30 #
# :. 30y=6(x+y) #
# :. 30y=6x+6y #
# :. 30y-6y=6x #
# :. 24y=6x #
# :. y=1/4x #

Now, # l=x+y #

#=> l=x+1/4x#
# :. l=5/4x#

Differentiating wrt #x# gives;

# (dl)/dx=5/4 #

And by the chain rule we have:

# (dl)/dt=(dl)/dx dx/dt #
# :. (dl)/dt=5/4 xx 2 #
# :. (dl)/dt=2.5 # feet/sec

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