# Finding a rocket's speed at height h

• meghanflowers
In summary, the problem involves finding the speed of a rocket at a given height if air resistance is neglected. The rocket has a mass of m and is launched straight up with a thrust of Fthrust. Using the relevant equations vfs^2=vis^2+2Δs and a=F/m, the initial velocity (vi) is substituted with 0 as the rocket is initially stopped. The expression for Vf is then derived as sqrt(2h(Fthrust/m)), where h represents the height at any given moment. However, the solution is incorrect as it does not account for the gravitational acceleration constant (g) and the change in mass of the rocket as it ascends. A Free Body Diagram of the rocket can

#### 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!

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
meghanflowers said:
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

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

topsquark