A street light is at the top of a 16 ft pole. A 5 ft tall girl walks along a straight path away from the pole with a speed of 3 ft/sec.

Question

At what rate is the tip of her shadow moving away from the light (ie. away from the top of the pole) when the girl is 36 ft away from the pole?

I know its last second but any help is appreciated

Answer 1

Make a sketch.
Let the length of the girl's shadow be x
let her distance from the lamp be y
so you have 2 similar triangles:
5/x = 16/(x+y)
5x + 5y = 16x
5y = 11x
5 dy/dx = 11 dx/dx
dy/dx = 11/5

so her shadow is increasing at 11/5 ft/sec or2.2 ft/sec
but it is moving at 11/5 + 3 or
26/5 ft/sec or 5.2 ft/s