A street light is at the top of a 13 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 35 ft from the base of the pole?
calculus - Steve, Saturday, November 26, 2011 at 5:12am
Let the woman be x feet from the pole, and the shadow tip be s feet in front of the woman.
By similar triangles,
s/6 = (x+s)/13
s = 6/7 x
ds/dt = 6/7 dx/dt = 6/7 * 7 = 6
The shadow is moving at 6ft/s from the woman, and she's moving 7ft/s from the pole.
so, the shadow moves at 13ft/s regardless of the distance from the pole.