During your summer internship for an aerospace company, you are asked to design a small research rocket. The rocket is to be launched from rest from the earth's surface and is to reach a maximum height of 950 m above the earth's surface. The rocket's engines give the rocket an upward acceleration so it moves with acceleration of 16.0 m/s2 during the time T that they fire. After the engines shut off, the rocket is in free fall. Ignore air resistance. Assume that the acceleration due to gravity does not change with the height of the rocket. Required:
What must be the value of T in order for the rocket to reach the required altitude?

T = 6.72 s

Explanation:

V(1) would be the final velocity of the rocket when it's engines are fired. This V(1) is also equal to the initial velocity of the rocket if it's engines gets shut down.

Also, y(1) is the distance that will be traveled by the rocket if the engines get shut down.

see attachment for calculations.

The first is upon firing of the rocket engines

The second is when the engines are down

The third is when the engines are fired.

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