Pretty sure I have every part of this problem solved but my final answer concerns me as it seems a little high.

for 0<=t<=3

and for t>3

I should find the maximum altitude and time in which it gets there. My answer is 56s and 18565.18meters.

**additional info**

initial velocity ( is 366.4m/s)

initial position ( ) is 0

after taking integral of v(t)

**

= position fxn until 3 seconds.

after 3 seconds of burn

=position fxn after 3s initial burn.

at t=56.2145s

where t=56.2145s

17087.98+1477.2=18565.18meters

Is it me or is that pretty dang high?