Question

A street light is at the top of a 27 ft pole. A 6 ft tall girl walks along a straight path away from the pole with a speed of 8 ft/sec.
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 23 ft away from the pole?
how fast is her shadow lengthening?

Answer 1

If her shadow has length s, then when she is x feet from the pole,
s/6 = (s+x)/27
s = 2/7 x
so,
ds/dt = 2/7 dx/dt = 2/7 * 8 = 16/7 ft/s
regardless of how far she is from the pole.

The tip of the shadow is moving at dx/dt + ds/dt = 8 + 16/7 ft/s