Answer:
110.9 feet
Step-by-step explanation:
The function that models the flight of the ball is
[tex]f(x) = - 0.02 {x}^{2} + 2.2x + 2[/tex]where f(x) is the vertical distance in feet and x is the horizontal distance the ball travels
If the ball hits the ground, then f(x)=0
[tex] \implies - 0.02 {x}^{2} + 2.2x + 2 = 0[/tex]
The solution is given by the quadratic formula:
[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
We substitute a=-0.02, b=2.2, and c=2 to get:
[tex]x = \frac{ - 2.2 \pm \sqrt{ {2.2}^{2} - 4 \times - 0.02 \times 2} }{2 \times - 0.02} [/tex]
This implies that:
[tex]x = 110.90 \: or \: x = - 0.90[/tex]
Since we are dealing with time,
[tex]x = 110.90[/tex]
To one decimal place, we have 110.9 feet
