How Do You Calculate Rocket Motion Parameters Over Time?

[Dulle]

Hi there
I'm having a bit trouble understanding the rocket motion and how the find the velocity, acceleration and travelheight as a function of time.
First, i assume that the velocity of the ejected mass relative to the rocket is constant. Secondly, i assume that the rocket mass changes with a constant rate. I'm working with the motion in a single dimension.

I have derived the rocket motion equation considering the acceleration of the rocket to be:

where vr is the velocity of the rocket, ve is the exhaust velocity, Mr is the mass of the rocket and dM/dt is the change in mass over the interval dt.

So - how do i find:

The velocity as a function of time
The acceleration as a function of time
The travelheight as a function of time

 

[SystemTheory]

For vertical motion you'll need to account for changing weight w = -mg and the drag, and then if the engine burn is short consider the momentum during coasting flight.. Start here and be sure to visit the NASA link included:

https://www.physicsforums.com/showthread.php?t=199087

 

[kerimek]

Hello there,

Understanding rocket motion can be a complex topic, but I will do my best to explain it in a clear and concise manner.

To find the velocity as a function of time, we can use the equation you have derived:

vr = ve * ln(Mr/M0)

Where Mr is the mass of the rocket at time t, M0 is the initial mass of the rocket, and ve is the exhaust velocity. This equation assumes that the velocity of the ejected mass relative to the rocket is constant, which is a reasonable assumption for most rockets.

To find the acceleration as a function of time, we can use the derivative of the velocity equation:

a = dvr/dt = ve * d(Mr/M0)/dt

This equation shows that the acceleration of the rocket is directly proportional to the change in mass over time. As the rocket burns fuel and loses mass, the acceleration will decrease over time.

To find the travel height as a function of time, we can use the equation for displacement in one dimension:

h = ho + v0t + (1/2)at^2

Where h is the travel height, ho is the initial height, v0 is the initial velocity, a is the acceleration, and t is the time. This equation assumes that the rocket is starting from rest at time t=0.

I hope this helps to clarify your understanding of rocket motion. Keep in mind that these equations are simplified and do not take into account factors such as air resistance, gravity, and the changing mass of the rocket. But they should give you a good starting point for understanding the basics of rocket motion. Best of luck with your studies!