A street light is mounted at the top of a 15-ft-tall pole.

Question

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 7 ft/s along a straight path. How fast is the tip of his shadow moving when he is 45 ft from the pole?

Answer 1

Let x is distance of man from the pole. If l is length of shadow. Then from similyariti of triangles we have:

l/(l + x) = 6/15 or l/(l + x) = 2/5; 5l = 2l + 2x, l = 2/3x.

Now speed of the tip of shadow is dl/dt = 2/3dx/dt = 2/3 = 2/3(7) = 14/3 ft/s