Question

shadow A street light is at the top of a 20 ft tall pole. A woman 4 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 ft from the base of the pole? Round to two decimal places .

Answer 1

We have a pole that is 20 ft tall, and a woman who is 4 ft tall. The woman is walking away from the pole with a speed of 6 ft/sec. We want to find out how fast the tip of her shadow is moving when she is 45 ft from the base of the pole.

To solve this, we can use similar triangles. The height of the pole, the height of the woman, and the length of her shadow form a set of similar triangles. This means that the ratios of corresponding sides are equal.

Let's call the distance between the woman and the pole "x". Using the similar triangles, we can set up the following proportion:

(20 ft + 4 ft) / x = 20 ft / (x + 45 ft)

By solving this proportion, we can find the value of "x". Once we have the value of "x", we can differentiate the equation with respect to time to find the rate at which the tip of her shadow is moving.