A spotlight on the ground shines on a wall 12 m away.

Question

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.1 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?

Answer 1

I will solve without picture. Let x is distance from Man to building. Then from cimilyarity of triangles we have:

(12 - x)/12 = 2/h, where h is length of shadow. So h = 24/(12 - x).

Now dh/dt = 24/(12 - x)²dx/dt = 24/12 - 4)²· 1.1 = 0.4125 m/s