A street light is at the top of a 19 foot tall pole. A 6 foot tall woman 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 35 feet from the base of the pole?
Let's assume that the shadow of the woman is cast in a straight line. At any given time, let's say the distance from the woman to the pole is x feet. Therefore, the length of her shadow is (x + 19) feet.
We are given that the woman is walking away from the pole with a speed of 4 ft/sec. Therefore, the rate of change of x is dx/dt = 4 ft/sec.
We need to find the rate of change of the length of the shadow with respect to time, which is d(x + 19)/dt.
Using the chain rule, we can differentiate the equation (x + 19) with respect to t:
d(x + 19)/dt = dx/dt + 0 = 4 + 0 = 4 ft/sec.
Therefore, the tip of her shadow is moving at a constant rate of 4 ft/sec.