Street Light
Posted in Garden Antiques on 01/11/2011 12:32 pm by adminrelated rate problem. A street light is at the top of a 20 ft tall pole. A woman 6 ft tall walks away from the?
A street light is at the top of a 20 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 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?
The height of the shadow can be described as a function of the distance from the pole:
20' / (x+h) = 6 / h
20h = 6x + 6h
14h = 6x
Where x is the distance from the pole and h is the height of the shadow. Therefore:
h = (6/14) * x
dh/dt = (3/7) * dx/dt
dh/dt = (3/7) * (4 ft/s) = 12/7 ft/s
BUT - she is also moving at 4 ft/s, so the tip of the shadow is moving at 4 + 12/7 = 5 + 5/7 ft/s
It turns out that the distance from the pole doesn't matter in this case.