Calculating Total Flight Time for a Rocket: A Scientific Approach

[ColeridgianHam]

Homework Statement

A missile silo is used to launch interplanetary rockets vertically upward out of the silo, giving the rocket an initial speed of 80.2 m/s at ground level. As the rocket clears the silo, the engines fire, and the rocket accelerates upward at 3.80 m/s^2 until it reaches an altitude of 1,080 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of −9.80 m/s^2.
Determine the rocket's velocity (in m/s) just before ground impact and its total time of flight (in s).

Relevant Equations

t=(Vx-Vi)/a

I calculated the time for the velocity before ground impact, which is v = -189.23 and the velocity at end of engine burn time, which is 120.996. I also calculated the max altitude (y = 1826.94), and the time to reach the max altitude was t = 23.0823 seconds. So from this information, I did:
t = (-189.23 + 120.996)/-9.80 = 6.9626 seconds.
Since the question asked for total flight time, I added this time together with the time to reach the maximum altitude:
6.9626s + 23.0823s = 30.0449 seconds
However, I was told my calculation for the total flight time is wrong, while everything else is correct. Where did I mess up?

 

[anuttarasammyak]

The rocket has initial velocity 80.2 m/s at groud level when t=0 s and go up to 1080 m with acceleration 3.80 m/s^2. When , say t1, the rocket reached height 1,080 m ?. How much speed, say v1, does it have then?

The rocket free falls with initial velocity v1 with gravity g downward at t=t1 second. When, say t2, the rocket crash to ground ? How much speed, say v2, does it have then?

 

[mjc123]

t = (-189.23 + 120.996)/-9.80 = 6.9626 seconds.
Since the question asked for total flight time, I added this time together with the time to reach the maximum altitude:

But t is not the time to fall from max altitude. What is the velocity at max altitude?

 

[jbriggs444]

t = (-189.23 + 120.996)/-9.80 = 6.9626 seconds.

This figure is supposed to have been the time taken for the Earth's gravity to reverse a 120.996 meter per second upward velocity into a -189.23 meter per second downward velocity.

Can you see a sign error in the calculation?

 

[haruspex]

But t is not the time to fall from max altitude. What is the velocity at max altitude?

Your point is valid, but having corrected the calculation of that t (per post #4) it would be simpler to consider what time should be added to it to get the total flight time.