The law of an object moving with constant acceleration is
Where is space,
is time,
is the initial position,
is the initial velocity and
is the acceleration.
In this case, if we choose a reference grid with the vertical axis pointing upwards, the acceleration of gravity will point downwards (and thus be negative). The initial position is zero, because the rocket is on the ground, and the initial velocity is 100 (positive because pointing upwards).
So, its law is
(I changed for
since the rocket is moving vertically, so its position is actually its height. Also, g is the acceleration due to gravity).
The rocket hits the ground if its height is zero, so if we set we have
Solving for t, we have either t=0, or
The solution t=0 means that at the beginning the rocket is on the ground. So, we're interested in the other solution. Considering that g is about 32.2 feet/s^2, we have