Question

A football player kicks a football downfield. The height of the football increases until it reaches a maximum height of 20 yards, 20 yards away from the player. A second

kick is modeled by f (x) = -0.037x(x – 45), where f is the height (in yards) and x is the horizontal distance (in yards). Compare the distances that the footballs
travel before hitting the ground.
The
kick travels farther before hitting the ground.
The kick travels
yards farther.

Answer 1

The first and second kick travels the same distance before hitting the ground.

Step-by-step explanation:

In order to compare the distances that the footballs travel before hitting the ground, we need to determine when the second kick reaches the ground. We can do this by finding the roots of the equation f(x) = -0.037x(x - 45), which represents the height of the football at different distances.

Setting the equation equal to 0, we get -0.037x(x - 45) = 0. Solving for x, we find that x = 0 and x = 45. This means that the football hits the ground at distance x = 0 and x = 45 yards.

Therefore, the first kick travels a total distance of 45 yards before hitting the ground, while the second kick travels a total distance of 45 yards as well. Therefore, the two kicks travel the same distance before hitting the ground.