6*9/4 A street light is at the top of a 20 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 feet from the base of the pole?

Question

Mathematics

Barnaby

10 August, 01:27

6*9/4 A street light is at the top of a 20 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 feet from the base of the pole?

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Mariela Short · Answer 1

10 ft/sec

Step-by-step explanation:

Consider the triangle formed by the top 14 ft of the light pole, the line parallel to the ground to the woman's head, and the line from her head to the light.

That triangle is similar to the one formed by the light pole, the line across the ground from the pole to the shadow tip, and the line from the tip of the shadow to the light.

The latter triangle is 20/14 times the former in size, so the distance from light pole to shadow tip is 20/14 = 10/7 times the distance of the woman from the light.

Then the rate of movement of the shadow tip is 10/7 times the rate of change of distance of the woman from the light:

(10/7) * (7 ft/sec) = 10 ft/sec