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posted by Taylor .
A model rocket is launched straight upward with an initial speed of 30.0 m/s. It accelerates with a constant upward acceleration of 2.50 m/s2 until its engines stop at an altitude of 160 m.
A. what is the maximum height reached by the rocket?
B. how long does the rocket stay in the air?

First find the time and velocity when the rocket stops accelerating ("burnout"). Then write equations for altitude and velocity vs time for times after burnout.
Maximum altitude will be obtained at the time when the velocity is zero, after burnout.
Solve the altitudetime equation for the additional afterburnout time it takes for the rocket to hit the ground. Be sure to add the time spent accelerating to get the total time aloft.
Someone will gladly critique your work. 
1103.4

A,h=23m B.56m
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