A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 75.5 m/s2 for 1.58 seconds, at which point its fuel abruptly runs out. Air resistance has no effect on its flight. What maximum altitude (above the ground) will the rocket reach?

Answer 1

the rocket attains a velocity of
75.5 * 1.58 or 119.3 m/s

since it started from zero, the average velocity for the 1st part of the flight is 119.3/2 or 59.65 m/s

it runs out of fuel at a height of
1.58 * 59.65 or 94.24 m

in the 2nd part of the flight, the rocket is decelerated by gravity for
119.3 / 9.8 or 12.17 s

since the rocket is slowing back to zero (at max height), the average velocity is the same as during the 1st part of the flight

the height from fuel exhaustion to peak is 59.65 * 12.17 or 725.94 m

the max altitude is
94.24 m + 725.94 m or 820. m