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
Nov 2, 2016
Explanation:
Let the man be
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+1/4x#
# :. l=5/4x#
Differentiating wrt
# (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