Before the engines fail, the rocket's altitude at time <em>t</em> is given by
and its velocity is
The rocket then reaches an altitude of 1150 m at time <em>t</em> such that
Solve for <em>t</em> to find this time to be
At this time, the rocket attains a velocity of
When it's in freefall, the rocket's altitude is given by
where 
is the acceleration due to gravity, and its velocity is
(a) After the first 11.2 s of flight, the rocket is in the air for as long as it takes for 
to reach 0:
So the rocket is in motion for a total of 11.2 s + 32.6 s = 43.4 s.
(b) Recall that
where 
and 
denote final and initial velocities, respecitively, 
denotes acceleration, and 
the difference in altitudes over some time interval. At its maximum height, the rocket has zero velocity. After the engines fail, the rocket will keep moving upward for a little while before it starts to fall to the ground, which means 
will contain the information we need to find the maximum height.
Solve for 
and we find that the rocket reaches a maximum altitude of about 1930 m.
(c) In part (a), we found the time it takes for the rocket to hit the ground (relative to ) to be about 32.6 s. Plug this into 
to find the velocity before it crashes:
That is, the rocket has a velocity of 196 m/s in the downward direction as it hits the ground.
