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 4 ft/s along
a straight path. how fast is the tip of his shadow moving when he is 30 ft from the pole?
1 answer:
Answer: 2.67 ft/s
Explanation:
1) The diagram with the triangle that represents the situation is in the image attached.
2) Similarity properties
(x + y) / 15 = y/6
⇒ 6(x+y) = 15y
⇒ 6x + 6y = 15y
⇒ 6x = 15y - 6y
⇒ 6x = 9y
⇒ y = 6x / 9
⇒ y = 2x / 3
3) Velocity is the derivative respecto to time. Then, find the derivative respect to time, t, on both sides
dy/dt = (2/3)dx/dt
4) The statement tells v = dx/dt = 4 ft/s
⇒ dy/dt = (2/3) 4 ft/s = (8/3)m/s ≈ 2.67 ft/s
Notice that this speed is constant, it does not depends upon the distance of 30 ft.
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