Finding max height for a rocket with upwards acceleration

[garcia1]

Homework Statement

A toy rocket, launched from the ground, rises
vertically with an acceleration of 23 m/s2 for
11 s until its motor stops.
Disregarding any air resistance, what max-
imum height above the ground will the rocket
achieve? The acceleration of gravity is
9.8 m/s2 .
Answer in units of km.

Homework Equations

I used kinematics equation: x=Vo*t + 1/2at^2

The Attempt at a Solution

I was a little unsure how to go about this problem, since most free fall problems I've dealt with use only gravity as acceleration.

I tried plugging the following values into my equation:
Vo = 0m/s
a = 23 m/s^2
t = 11s

I got the answer 1391.5m, but this was wrong. I think the problem is simpler than I'm thinking about it, but I can really use some help on this.

 

[tiny-tim]

hi garcia1!

(try using the X² and X₂ icons just above the Reply box )

I tried plugging the following values into my equation:
Vo = 0m/s
a = 23 m/s^2
t = 11s

I got the answer 1391.5m …

that's the height at the end of the first stage …

you still need the extra height that it goes with a = -9.81 m/s²

 

[garcia1]

So what I did next is solve for the final velocity of part 1 by using the fact that Vo = 0m/s since the rocket starts from rest. Using the equation V = Vo + at, I got the equation

V = 23*11 = 253m/s

With this I placed this final velocity as the initial velocity for the next segment. I determined in this 2nd segment that X = ?, Vo = 253m/s, a = -9.81m/s^2, and Vf = 0, since the rocket must come to rest at the final height before falling.

I got the following equation:
Vf^2 = Vo^2 + 2ax -> x = Vf^2 - Vo^2 / 2a.

This answer was 3265.76m. Adding this to the initial 1391.5m, I got 4657.27m. This was wrong though, so I think there is something in this second step I'm getting wrong. Any thoughts?

 

[gneill]

Did you answer in terms of km, or in terms of m?

 

[tiny-tim]

hi garcia1!

(just got up :zzz: …)

looks ok to me

but you should only be using two https://www.physicsforums.com/library.php?do=view_item&itemid=523"

(and as gneill says, the question does specify km )