m_{i} | Initial mass |
v_{i} | Initial velocity |
m_{f} | Final mass |
v_{f} | Final velocity |
e | Energy (J) available from fuel combustion |
[jstex]\frac{1}{2}m_i v_i^2 - \frac{1}{2}m_f v_f^2 = e[/jstex] | Equ. 1 |
[jstex]\frac{1}{2}m_f v_f^2 = \frac{1}{2}m_i v_i^2 - e[/jstex] | |
[jstex]v_f^2 = \frac{2 ( 1/2 m_i v_i^2 - e ) }{m_f}[/jstex] | |
[jstex]v_f = \sqrt{ \frac{m_i v_i^2 - 2e}{m_f} }[/jstex] | Equ.2 |
Copied for testing...
OK, looking up the LaTex, I can do Heiwa's equations in a more readable form. This gives another way of looking at the problem.
So, given:
m_{i} Initial mass v_{i} Initial velocity m_{f} Final mass v_{f} Final velocity e Energy (J) available from fuel combustion
[jstex]\frac{1}{2}m_i v_i^2 - \frac{1}{2}m_f v_f^2 = e[/jstex] Equ. 1
So, solving for v_{f}:
[jstex]\frac{1}{2}m_f v_f^2 = \frac{1}{2}m_i v_i^2 - e[/jstex] [jstex]v_f^2 = \frac{2 ( 1/2 m_i v_i^2 - e ) }{m_f}[/jstex] [jstex]v_f = \sqrt{ \frac{m_i v_i^2 - 2e}{m_f} }[/jstex] Equ.2
Heiwa, do you:
- Agree that this is correct?
- Agree that using Equ. 2, we can calculate the spacecraft's final velocity, given the initial velocity and mass, the final mass, and the energy from the burned fuel?
Observed result: Preview shows raw jstex.