Answer:
The time interval the rocket is in motion above the ground is the time in the two times the motion is going on

Step-by-step explanation:

The motion in the first step has an acceleration

and the maximum height will be and the end of this step is
So to know the time until the rocket fail and change the acceleration:


you can divide the expression by two and simplify the calculating


Using quadratic equation :



The time can be negative so, the time we are going to use is 10s

Now when the rocket fail it change the direction of the motion and the time is going to be the time it takes to reach earth again







The time can be negative so, the time we are going to use is 13,14s
So the full time is the both times adding them
