A rocket moves upward starting from rest with an acceleration of 32.5 m/s^2 for 4.52s. It runs out of fuel at the end of the 4.52 s but does not stop. How high does it rise above the ground?
The vertical velocity at burnout is 4.52(32.5) = 146.9m/s.
The burnout altitude derives from
h1 = 32.5[(4.52)^2]/2 - 9.8[(4.52)^2]/2 = 231.88m.
The coast time derives from 0 = 146.9 - 9.8t or t = 15sec.
The coast distance is therefore
h2 = 146.9(15)^2 - 4.9(15)^2 = 1101m.
h1 + h2 = 1332.88 meters.