Finding a rocket's speed at height h

[meghanflowers]

Homework Statement

A rocket of mass m is launched straight up with thrust Fthrust.
Find an expression for the rocket's speed at height h if air resistance is neglected.
Express your answer in terms of the variables Fthrust , m , h , and appropriate constants.

Relevant Equations

vfs^2=vis^2+2Δs
a=F/m

I substituted 0 for vi, as the rocket is initially stopped.
I am looking for Vf.
So:
Vf^2=0+2asΔs
Vf^2=2asΔs

I then substituted a=Fthrust/m

So:
Vf^2=2(Fthrust/m)Δs
Δs at any given moment equals h so I substituted h for Δs.
Then took the square root of both sides.
Vf=sqrt(2h(Fthrust/m))

It says it is wrong, and that the correct answer includes the gravitational acceleration constant(g).
I am really stuck. Thanks for helping!

 

[berkeman]

Welcome to PF.

It does look like you have not included the downward force due to gravity in your net force equation. Can you try including it?

Also, see the LaTeX Guide link below the Edit window to learn how best to post math equations at PF.

 

[topsquark]

Homework Statement:: A rocket of mass m is launched straight up with thrust Fthrust.
Find an expression for the rocket's speed at height h if air resistance is neglected.
Express your answer in terms of the variables Fthrust , m , h , and appropriate constants.
Relevant Equations:: vfs^2=vis^2+2Δs
a=F/m

I substituted 0 for vi, as the rocket is initially stopped.
I am looking for Vf.
So:
Vf^2=0+2asΔs
Vf^2=2asΔs

I then substituted a=Fthrust/m

So:
Vf^2=2(Fthrust/m)Δs
Δs at any given moment equals h so I substituted h for Δs.
Then took the square root of both sides.
Vf=sqrt(2h(Fthrust/m))

It says it is wrong, and that the correct answer includes the gravitational acceleration constant(g).
I am really stuck. Thanks for helping!

Big hint: Start by sketching a Free Body Diagram of the rocket.

-Dan

 

[erobz]

This is also ignoring the change in mass of the rocket as it ascends.