A spotlight on the ground shines on a wall 12 m away. If a man 2m tall walks fro

Question

A spotlight on the ground shines on a wall 12 m away. If a man 2m tall walks from the spotlight toward the building at a speed of 1.6 m/s how fast is the length of his shadow on the building decreasing when he is 4 m from the building?

The answer to this is 0.6 m/s. This same question has been posted by other people yet only one answer was right that I saw. They didn't give good work showing how step by step to get to the answer so I'm hoping that someone could explain it better and show all the steps I need to solve this and simply.

Explanation / Answer

1. A spotlight on the ground shines on a wall 12 m away Let x be the distance of the light to the man, Let s be the shadow cast on the building excluding the 2 m and the distance from the man to the building is 12-x We have two similar triangles: 2/x = s/(12-x) 24 + 2x = sx 2 dx/dt = s dx/dt + x ds/dt when the man is 4m from the building , 12-x = 4, x = 8 2/x = s/(12-x) becomes 2/8 = s/(12-8) 1/4 = s/4 s = 1 2 dx/dt = s dx/dt + x ds/dt becomes 2 (1.6) = 1 (1.6) + 8 ds/dt ds/dt=1.6/8 ds/dt=0.2

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