# Kinematics in 1D - Model Rocket Question

1. Sep 27, 2009

### crono_

1. The problem statement, all variables and given/known data

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 =

2. Relevant equations

Eq 1: Vf = Vo + at

Eq 2: x = Vot + 1/2 at2

3. 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?

2. Sep 27, 2009

### 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.

3. Sep 27, 2009

### 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?