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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We can see that the magnitude of the force is directly proportional to the charges. This means that when one of the charges is doubled, the magnitude of the electrostatic force will double as well, so the correct answer is
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