find max height, how long after lift off does rocket reach it's maximum height, how long is rocket in air?

Question

rocket launched upward with initial speed of 50m/s and constant acceleration of 2m/s2 with altitude of 150 m

Answer 1

By 2 m/s^2 acceleration I assume you mean the upward thrust acceleration that opposes g, because if you meant total acceleration the rocket would keep rising forever.
v0 = 50; h0 = 150; a(thrust) = 2
t = v0/g
downward acceleration a = g-a(thrust)
hmax = h0 + v0t - at^2/2