The equation given in the question is
h(t)= -16t^2+144
When the height becomes zero, then
- 16t^2 + 144 = 0
16t^2 = 144
(4t)^2 = (12)^2
4t = 12
t = 3
From the above deduction, it can be easily concluded that the correct option among all the options that are given in the question is the fourth option or option "D". I hope that this is the answer that has actually come to your desired help.