A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 16 ft from the lamppost?

1 Answer
Jan 19, 2018

The length of the shadow is changing at #=2.69(ft)/sec#

Explanation:

Let the distance of the person from the bottom of the light post be #=x ft#

And the length of his shadow is #=y ft#

Form the similar triangles

#(x+y)/(20)=y/7#

#7(x+y)=20y#

#7x+7y=20y#

#13y=7x#

#y=7/13x#

Differentiating wrt #t#

#dy/dt=7/13dx/dt#

We know that #dx/dt=5(ft)/sec#

Therefore,

#dy/dt=7/13*5=35/13=2.69(ft)/sec#