Question

A street light is at the top of a 16 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 along the ground when she is 50 ft from the base of the pole?

Answer 1

The tip of the woman's shadow is moving along the ground at a rate of 0.48 ft/sec.

Step-by-step explanation:

To solve this problem, we can use similar triangles and the concept of similar triangles. Let's call the distance of the woman from the base of the pole x and the length of her shadow y. Using the concept of similar triangles, we can set up the following proportion:

(y + 6) / x = y / 50

Simplifying this proportion, we get:

y = (x * 6) / 50

Now, we can differentiate both sides of this equation with respect to time to find the rate at which y is changing:

dy/dt = 6/50 * dx/dt

Given that dx/dt is 4 ft/sec, we can substitute this value into the equation:

dy/dt = (6/50) * 4 = 24/50 = 0.48 ft/sec

So, the tip of her shadow is moving along the ground at a rate of 0.48 ft/sec.

Answer 2

4 ft/sec

Step-by-step explanation:

Given:

16 ft = height of a street light on top of a pole

6 ft = height of a woman

4 ft/s = speed that the woman is walking away from the pole along a straight path

50 ft = distance of woman from the pole at the specific time they want to know the speed of the tip of the man's shadow.

solution:

A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. if we let t be the time in seconds and x be the distance from the pole to the woman in ft then we are given that dx/dt=4 ft/sec