Question

a light sitting on the ground is shining onto a wall 20 feet away from the light. if a 5 foot person is walking toward the light at 4 ft/sec., how fast is the shadow moving up or down the wall when he is 15 feet from the wall?

Answer 1

Let x be the distance from the person to the light. Let h be the height of the shadow on the wall.
using similar triangles,

h/20 = 5/x

h'/20 = -5/x^2 x'
h'/20 = -5/25*(-4) = 4/5
h' = 16

so, the shadow is moving up the wall at 16ft/sec