Kinematics in 1D - Model Rocket Question

[crono_]

Homework Statement

A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 76.0 m/s2 for 1.54 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?

Segment 1

Known Values:

Vo₁ = 0 m/s

a₁ = 76.0 m/s²

t₁ = 1.54 s

Unknown Values:

Vf₁ =

x₁ =

Segment 2

Known Values:

a₂ = -9.80 m/s²

Unknown Values:

Vo₂ = Vf₁ =

Vf₂ =

t₂ =

x₂ =

Homework Equations

Eq 1: Vf = Vo + at

Eq 2: x = volt + 1/2 at²

The Attempt at a Solution

I broke the question up into two segments. It was pretty easy to find the unknowns in the first segment.

Using Eq 1, I found Vf₁ to be 117 m/s

Using Eq 2, I found x₁ to be 90.1 m

Vf₁ will be = to Vo₁. But I'm left finding Vf₂, t₂ and x₂. I'm stuck because to find x₂ I need t₂...but to find t₂, I'm pretty sure I need x₂. And naturally Vf₂ would be helpful as well...

a = $$\Delta$$v / $$\Delta$$t

But I don't have t or Vf so I don't think I can use that here...

Any suggestions?

 

[crono_]

Wait...just had a realizing. Vf₂ will = 0 m/s as it reaches the top of the rockets height. That big of info may help me figure the rest out.

That said, if anyone has any comments or anything they'd like to share that would be appreciated.

 

[crono_]

Seeing as how Vf₂ = 0 m/s, I can use this to obtain t₂.

a = $$\Delta$$v / t

t = $$\Delta$$v / a

t = 0 m/s - 117 m/s / -9.8 m/s²

t = 11.9 s

With having found t₂, I can use x = 1/2 (Vo + Vf) t

x = 1/2 (117 m/s) 11.9 x

x = 696 m

So, max alt would be 696 m + 90.1 m = 786 m

Am I correct?