Question

The function y=-0.4x² +60x models the height y, in feet, of a cannonball, where x is the horizontal distance, in feet, from where it was fired. How many feet did the cannonball fly before it hit the ground?

Answer 1

The cannonball flew 150 feet before it hit the ground. This result is obtained by setting the height equation to zero and solving for the horizontal distance x.

Step-by-step explanation:

To determine how many feet the cannonball flew before it hit the ground using the given function y = -0.4x² + 60x, you need to find the value of x when y equals zero, as this represents the height. The cannonball hits the ground when its height, y, is 0 feet.

Setting the function equal to 0 and solving for x, we have:

0 = -0.4x² + 60x

Dividing all terms by -0.4 gives us:

0 = x² - 150x

Factoring out x gives us:

0 = x(x - 150)

Setting each factor equal to zero gives us two solutions:

• x = 0 (where the cannonball was fired)
• x = 150 (where the cannonball hits the ground)

Therefore, the cannonball flew 150 feet before it hit the ground.