A street light is at the top of a 12 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving along the ground when she is 50 ft from the base of the pole?

Question

Kinsley Delacruz

Mathematics

18 November, 12:15

A street light is at the top of a 12 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving along the ground when she is 50 ft from the base of the pole?

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Answers (1)

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Rodolfo Rocha · Answer 1

10ft/sec

Step-by-step explanation:

In t sec the lady would be at a distance of (speed) (time) = (5 ft/sec) (t sec) = 5t ft.

As the height of the pole is double the height of the lady, from similar triangles, we can deduct the tip of the shadow would be at a distance x = 2 (5t) ft = 10t.

The distance equation is x = 10t ft.

So, the speed is x' = 10 ft/sec.

The speed will be constant like the speed of the lady.