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?

Question

Nora Escobar

Mathematics

18 April, 08:55

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?

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Answers (1)

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Arjun Wang · 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.