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

Mathematics

Rowan Dickerson

5 March, 03:10

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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Lucas · 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.