Question

A street light is mounted at the top of a 15-ft tall pole. A man 6 ft tall walks away from the pole with a speed of 5 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole?

Answer 1

Let d=distance
and
x = length of shadow.
Therfore,
x=(d + x)
= 6/15
So,
15x = 6x + 6d
9x = 6d.
x = (2/3)d.

As we know that:
dx=dt
= (2/3) (d/dt)
Also,
Given:
d(d)=dt
= 5 ft/s
Thus,
d(d + x)=dt
= (5/3)d (d/dt)
Substitute, d= 5
d(d + x) = 25/3 ft/s.
Hence,
d(d + x) = 8.33 ft/s.