How Do You Calculate Rocket's Maximum Height and Velocity?

[monocomprendo]

Homework Statement

A rocket launched vertically takes 6.13 seconds in total. How much time does it take the rocket to reach its maximum height. What is the velocity of the rocket in meters per second at maximum height? What is the initial velocity of the rocket. Give your answer in meters per second.

Homework Equations

final velocity = initial velocity + (acceleration x time)
distance = 1/2 x (initial velocity + final velocity) x time
distance = initial velocity x time + 1/2 acceleration x time^2
final velocity^2 = initial velocity^2 + 2 x acceleration x distance

The Attempt at a Solution

I feel as though there is not enough information. I am not sure, but is the time it takes to reach the maximum height just half of the total time? Which would be 3.07 (rounded) seconds. So then I can use the kinematic equations to try to solve for the rest. Distance = initial velocity x time + 1/2(acceleration) x time^2 so d=0+ (9.8 x 3.07^2). So distance = 92.4 meters?

 

[haruspex]

I agree, it doesn't seem like enough information for the first question. But do what you can by plugging in variables for the unknowns, like rocket mass and fuel mass, etc. Who knows, maybe those will magically go away.
Max height would be at half time if it were just a projectile, but rockets typically burn fuel during part of the ascent, both accelerating them and making them lighter.
(Of course, if it burnt all the fuel very quickly, accelerating it hugely, it would then approximate a projectile. This almost convinces me there's not enough info.)

OTOH, you have more than enough information to answer the last two questions.