Finding a rocket's speed at height h

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
  • #1
meghanflowers
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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!
 
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  • #2
Welcome to PF. :smile:

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. :smile:
 
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  • #3
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
 
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  • #4
This is also ignoring the change in mass of the rocket as it ascends.
 
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What is the formula for finding a rocket's speed at height h?

The formula for finding a rocket's speed at height h is v = √(2gh), where v is the speed, g is the acceleration due to gravity, and h is the height.

How does the acceleration due to gravity affect a rocket's speed at height h?

The acceleration due to gravity affects a rocket's speed at height h by increasing the speed as the rocket moves closer to the ground. This is because the force of gravity pulls the rocket towards the ground, increasing its velocity.

What units should be used for height and speed in the formula?

The units for height should be in meters (m) and the units for speed should be in meters per second (m/s) in order to get the correct result. It is important to use consistent units in order to avoid errors in the calculation.

Can the formula be used for any type of rocket?

Yes, the formula for finding a rocket's speed at height h can be used for any type of rocket as long as the acceleration due to gravity is constant and the rocket is moving vertically. However, the formula may not be accurate for rockets that experience significant air resistance or those that change direction during flight.

What are some factors that can affect a rocket's speed at height h?

Some factors that can affect a rocket's speed at height h include the rocket's initial velocity, the angle of launch, the presence of air resistance, and external forces such as wind or thrust. These factors can impact the acceleration and velocity of the rocket as it moves through the air.

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