Question

A football player kicks a football downfield. The height of the football increases until it reaches a maximum height of 15 yards, 30 yards away from the player. A second kick is modeled by $f\left(x\right)=-0.032x\left(x-50\right)$ , 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.

Answer 1

Answer:

kick 1 has travelled 15 + 15 = 30 yards before hitting the ground

so kick 2 travels 25 + 25 = 50 yards before hitting the ground

first kick reached 8 yards and 2nd kick reached 20 yards  

Step-by-step explanation:

1st kick travelled 15 yards to reach maximum height of 8 yards

so, it has travelled 15 + 15 = 30 yards before hitting the ground

2nd kick is given by the equation

y (x) = -0.032x(x - 50)

$y = 1.6 x - 0.032x^2$

we know that maximum height occurs is given as

$x = -\frac{b}{2a}$

$y = - \frac{1.6}{2( - 0.032)} = 25$

and maximum height is

$y = 1.6(25) - 0.032 (25)^2$

y = 20

so kick 2 travels 25 + 25 = 50 yards before hitting the ground

first kick reached 8 yards and 2nd kick reached 20 yards