We already know that it takes 5.0s for the rocket to get to 102.5m altitude. What is left for us to find is the time it takes for the rocket to get to its maximum altitude and then fall back to the earth. Since we know its initial velocity and position when the engines turn off, we know that it will have a total displacement of the negative value of its altitude when it hits the ground.
We now need to use the quadratic equation to solve for t.
We are only concerned with what happens after t=0, so it takes 10.4s for the rocket to go from when its engines stop until it hits the ground.
