Rocket Height as one-dimension motion

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SUMMARY

The discussion focuses on calculating the maximum height (H) reached by a rocket that accelerates upward with a constant net acceleration (a) until its fuel is exhausted at time (t1). The formula derived for maximum height is H = (1/2) * a * t1^2. For the specific case where the net acceleration is a = 3g (where g = 9.81 m/s²) and t1 = 5.00 s, the maximum height is calculated as H = (1/2) * (3 * 9.81 m/s²) * (5.00 s)², resulting in H = 367.875 m.

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A rocket, initially at rest on the ground, accelerates straight upward from rest with constant net acceleration a, until time t1, when the fuel is exhausted.

Find the maximum height H that the rocket reaches (neglecting air resistance).

Express the maximum height in terms of a, t1, and/or g. Note that in this problem, g is a positive number equal to the magnitude of the acceleration due to gravity.

That's part 1. Then comes:

If the rocket's net acceleration is a=3g for t1=5.00 s, what is the maximum height the rocket will reach? (Using 9.81 m/s^2 for g).
 
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Please first of all show your work.
 

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