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:
[tex]t=\frac{-b\pm\sqrt[]{b^{2}-4ac}}{2a}[/tex]In this case, a = 16, b = 36 and c = -18
[tex]\begin{gathered} t=\frac{-36\pm\sqrt[]{(36)^{2}-4(16)(-18)}}{2(16)} \\ t=\frac{-36\pm49.47}{32} \\ t_1=-2.67 \\ t_2=\text{0}.42 \end{gathered}[/tex]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.
