Question

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?

Answer 1

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`