Question

1. (5 points) The arc of a football thrown by Patrick Mahomes is modeled by the equation h=-16t2 + 36t + 6, where h = the height of the ball and t = the time in seconds. Will the ball reach a height of 24 feet?

Answer 1

In order to determine if the ball reaches the 24 ft, replace h = 24 and solve the quadratic equation. If the solutions are real, then, the ball does reach 24ft.

Proceed as follow:

h = 16t² + 36t + 6

24 = 16t² + 36t + 6

16t² + 36t + 6 - 24 = 0

16t² + 36t - 18 = 0

use he quadratic formula, given by:

`t=\frac{-b\pm\sqrt[]{b^(2)-4ac}}{2a}`

In this case, a = 16, b = 36 and c = -18

`\begin{gathered} t=\frac{-36\pm\sqrt[]{(36)^(2)-4(16)(-18)}}{2(16)} \\ t=(-36\pm49.47)/(32) \\ t_1=-2.67 \\ t_2=\text{0}.42 \end{gathered}`

negative times do not have physical meanning, then, the available solution is

t = 0.42

Hence, you can conclude that the ball reaches 24 ft for a time of 0.42 seconds.