what speed is the shadow moving?

Question

A street light is on top of a 10 foot pole. Mario, who is 6 feet tall, walks away from the pole at a rate of 4 feet per second. At what speed is the tip of Mario's shadow growing when he is 10 feet from the pole?

Answer 1

It's growing at a rate of 10 feet per second. Let x represent the distance between Mario and the wall, and let s represent the distance between the tip of Mario's shadow and the wall. By similar triangles, 6/10 = (s - x)/s. Thus s = (5/2)x. Taking derivatives, one finds that the tip of Mario's shadow is growing at a rate of ds/dt = (5/2)dx/dt = (5/2)(4 ft/s) = 10 ft/s.