A street light is at the top of a "20" 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 when she is "50" ft from the base of the pole?

Question

Ace Small

Mathematics

4 March, 02:30

A street light is at the top of a "20" 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 when she is "50" ft from the base of the pole?

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Answers (1)

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Jair Chan · Answer 1

Height of Woman, w = 6 ft.

Distance Between Woman and Pole, s = 35 ft.

Speed of Woman, ds/dt = 5 ft./sec

Length of Shadow = L

Distanc Between Woman and End of Shadow = x

p / (s + x) = w / x

13 / (35 + x) = 6 / x

13x = 6 (35 + x)

13x = 210 + 6x

13x - 6x = 210

7x = 210

x = 210 / 7

x = 30

L = s + x

L = 35 + 30

L = 65

p / L = w / (L - s)

13 / L = 6 / (L - s)

13 (L - s) = 6L

13L - 13s = 6L

13L - 6L = 13s

7L = 13s