Acatapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 80.0 m/s at ground level. the engines then fire, and the rocket accelerates up- ward at 4.00 m/s2 until it reaches an altitude of 1 000 m. at that point, its engines fail and the rocket goes into free fall, with an acceleration of 29.80 m/s2. (a) for what time interval is the rocket in motion above the ground?

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

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

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