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?

Answer 1

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.