A model rocket is launched straight upward

Question

with an initial speed of 53.0 m/s. It acceler-
ates with a constant upward acceleration of
3.21 m/s2 until its engines stop at an altitude
of 230 m.
What is the maximum height reached by
the rocket? The acceleration of gravity is
9.81 m/s2.
Answer in units of

Answer 1

two phases, accelerating up and coasting up

acceleration phase:
V = Vi + a t
h = Vi t + (1/2) a t^2

230 = 53 t + 1.605 t^2
solve this quadratic equation for t
then v at 230 m = 53 + 3.21 t

Now phase 2, coasting up from 230 m with new Vi and acceleration = -9.8 m/s
Vi = the v we just got from phase one.
final v at top = 0
so
0 = Vi - 9.8 t
solve for t
then
h = 230 + Vi t - 4.9 t^2
Vi =