Acceleration, velocity and position of a rocket

  • Thread starter Belginator
  • Start date
  • #1
12
0
Hi everyone,

Quick question I may just not be thinking right here but I was trying to find the acceleration, velocity, and position of a rocket as a function of time. I started with acceleration:

[itex]a =\frac{T}{m-\dot{m}t} - g[/itex] where T is the Thrust, m is the initial mass, mdot is the mass flow rate, and g is gravity. This equation seems to work out with dimensional analysis and logically it seems to make sense, but maybe I'm wrong there. So from there I integrated wrt to time to get the velocity:

[itex]v = -\frac{T}{\dot{m}} ln(m-\dot{m}t) -gt + v_0 [/itex] Here is where the problem comes in, while I'm pretty sure I did my integration right, the units don't work out properly and velocity doesn't start out at 0 either, unless you set the [itex] v_0 [/itex] term to some value. Finally I tried to get position by integrating v:

[itex]s = \frac{T}{\dot{m}^2} ((m-\dot{m}t)ln(m-\dot{m}t) - (m-\dot{m}t)) - 0.5gt^2 + v_0t + s_0 [/itex] Again the units don't work out properly.

I'm just considering where the rocket goes vertical for now, no horizontal components.

What am I not seeing here? This should be fairly straight forward. Thanks in advance for any help.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
251
Hi Belginator! :smile:
[itex]v = -\frac{T}{\dot{m}} ln(m-\dot{m}t) -gt + v_0 [/itex] Here is where the problem comes in, while I'm pretty sure I did my integration right, the units don't work out properly and velocity doesn't start out at 0 either, unless you set the [itex] v_0 [/itex] term to some value.
No, the units are fine.

ln has no units (like sin) …

your ln(m-m't) + vo is really ln((m-m't)/(mo)) for some constant mo :wink:
 

Related Threads on Acceleration, velocity and position of a rocket

  • Last Post
Replies
1
Views
637
  • Last Post
Replies
9
Views
17K
Replies
1
Views
850
Replies
14
Views
805
Replies
16
Views
4K
Replies
2
Views
950
Replies
9
Views
2K
  • Last Post
Replies
8
Views
958
  • Last Post
Replies
4
Views
4K
Top