A football player kicks a football downfield. The height of the football increases until it reaches a maximum height of 10 yards, 25 yards away from the player.

Question

A football player kicks a football downfield. The height of the football increases until it reaches a maximum height of 10 yards, 25 yards away from the player. A second kick is modeled by f(x)=−0.043x(x−60), 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.

Which kick traveled farther before hitting the ground?

The kick traveled how many yards further?

Answer 1

y = -0.043 x ( x - 60) , or y = -0.043 x² + 2.58 x set y = 10 yards, 10 = -0.043 x²+ 2.58 X,

Rearrange -0.043 x² + 2.58 x - 10 = 0, multiply by -1, 0.043 x² -2.58 x + 10 = 0, divide by 0.043,

x = - ( -60) ± √2669.6 / 2(1) = 60 ± √2669.6 / 2 , x = 55.83, and x = 4.17, the equation has two solutions for the same height = 10 yards, choose x = 55.83 yards,

The football in the model kick traveled further than the actual distance of 25 yards before it hit the ground.

The football in the model kick traveled a further distance by = 55.83 - 25 = 30.83 yards