A rocket is launched vertically with an acceleration of 20m/s^2. After two minutes its engines fail. Calculate the max height reached by the rocket and its total time in the air

Answer 1

after 120 seconds,
v = at = 20*120 = 2400 m/s
h = 1/2 at^2 = 1/2 * 20 * 120^2 = 144000 m
From that point, it is just a ballistic trajectory, and the height is just
h(t) = 144000 + 2400t - 4.9t^2
Now just find the vertex of that parabola, in the usual way.
Then solve for t when h=0

Answer 2

That value for t will be after the initial 120 seconds ...