Question

a boy flies a kite at a height of 150 feet. the wind carries the kite horizontally away from him at a rate of 6 ft/s. how fast is the distance between the boy and the kite changing when the kite is 250 feet away from him? round the answer to one decimal place.

Answer 1

The rate at which the distance between the boy and the kite is changing when the kite is 250 feet away is 0 ft/s.

Step-by-step explanation:

To find the rate at which the distance between the boy and the kite is changing, we can use the concept of related rates. Let's denote the distance between the boy and the kite as 'x' and the height of the kite as 'y'. We are given that the height of the kite, y, is constant at 150 feet, and the distance, x, is increasing at a rate of 6 ft/s. We want to find the rate at which x is changing when the kite is 250 feet away from the boy.

Using the Pythagorean theorem, we know that the distance between the boy and the kite can be expressed as:

x^2 + y^2 = 250^2

Plugging in the given values, we have:

x^2 + 150^2 = 250^2

Simplifying and differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) = 0

Now, solving for dx/dt, we have:

dx/dt = 0 / (2x) = 0

Therefore, the rate at which the distance between the boy and the kite is changing when the kite is 250 feet away is 0 ft/s.