Answer:
[tex]t = \frac{9}{2}\,s[/tex]
Step-by-step explanation:
The time required by the ball to return to the ground is determined by equalizing height to zero:
[tex]h(t) = -12\cdot t^{2} + 54\cdot t[/tex]
[tex]-12\cdot t^{2} + 54\cdot t = 0[/tex]
[tex]-6\cdot t \cdot (2\cdot t -9) = 0[/tex]
Roots are described below:
[tex]t_{1} = 0\,s[/tex]
[tex]t_{2} = \frac{9}{2}\,s[/tex]
The second one corresponds to the time when the ball is returning to the ground.
