A street light is at the top of a 14 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole?

Answer 1

Make your sketch, you will have a smaller right-angled triangle within a larger one.
They are similar.
At a time of t seconds, let the length of her shadow be x ft, let her distance from the lamppost be y ft
6/x = 14/(x+y)
14x = 6x + 6y
8x = 6y
4x = 3y
4 dx/dt = 3 dy/dt

given: dy/dt = 7 ft/s
find dx/dt

4dx/dt = 3(7)
dx/dt = 21/4 ft/s , notice that rate is constant, no matter where she is

So her shadow is lengthening at 5.25 ft/sec
but her shadow is moving at 5.25 + 7 or 12.25 ft/s

(think of a moving train at 60 km/h and you walking in the train in its direction
at 4 km/h, so you are moving at 64 km/h relative to the ground)