Step-by-step explanation:
[tex]h(t) = -5t^{2} + 15t[/tex]
To determine the time it takes for the ball to hit the ground, we need to figure out when [tex]h(t) = 0[/tex].
[tex]0 = -5t^{2} + 15t[/tex]
[tex]t^{2} - 3t = 0[/tex]
[tex]t(t - 3) = 0[/tex]
Separating this into two separate equations will give us the times that [tex]h(t) = 0[/tex]:
[tex]t = 0[/tex]
[tex]t - 3 = 0[/tex]
[tex]t = 3[/tex]
We can ignore [tex]t = 0[/tex] since that is the initial time that the ball is kicked from the ground, so the answer to the question is [tex]t = 3[/tex].
