a street light is mounted at the top of a 15 foot pole. A man 6 ft tall walks away from the pole wit a speed of 7 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole

16.3 ft/s

Explanation:

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

= 7 ft/s

Thus,

d (d + x) = dt

= (7/3) d (d/dt)

Substitute, d = 7

d (d + x) = 49/3 ft/s.

Hence,

d (d + x) = 16.3 ft/s.