Editing Jet force (section)

== Analysis with momentum ==
To calculate the speed of the vessel due to the jet force itself, analysis of [[momentum]] is necessary. Conservation of momentum<ref>{{Cite web |url=http://www.physicsclassroom.com/class/momentum/Lesson-2/Momentum-Conservation-Principle |title=Momentum Conservation Principle |website=The Physics Classroom |access-date=2016-11-06}}</ref> states the following:
<math display="block">m_1 v_1 + m_2 v_2 = m_1 v_{1f} + m_2 v_{2f}</math>

In this situation, m<sub>1</sub> represents the mass of the gas in the propulsion system, v<sub>1</sub> represents the initial speed of this gas, m<sub>2</sub> represents the mass of the rocket and v<sub>2</sub> represents the initial velocity of the rocket. On the other end of the equation, v<sub>1f</sub> represents the final velocity of the gas and v<sub>2f</sub> represents the final velocity of the rocket. Initially, both the gas in the propulsion system and the rocket are stationary, leading to v<sub>1</sub> and v<sub>2</sub> equaling 0. As such, the equation can be simplified to the following:
<math display="block">0 = m_1 v_{1f} + m_2 v_{2f}</math>

After some more simple algebra, we can calculate that v<sub>2</sub> (the velocity of the rocket) is the following:
<math display="block">v_{2f} = -\frac{m_1 v_1}{m_2}</math>

This gives us the velocity of the aircraft right after it takes off. Because we know all forces acting on it from this point on, we can calculate net acceleration using [[Newton's second law of motion|Newton's second law]].<ref>{{Cite web |url=http://www.livescience.com/46560-newton-second-law.html |title=Force, Mass & Acceleration: Newton's Second Law of Motion |website=Live Science |author=Jim Lucas |date=27 September 2017 |access-date=6 August 2023}}</ref> Given the velocity that the aircraft takes off with and the acceleration at any point, the velocity can also be calculated at any given point.<ref>{{Cite web|url=https://www.khanacademy.org/science/physics/one-dimensional-motion/kinematic-formulas/a/what-are-the-kinematic-formulas |title=What are the kinematic formulas? |publisher=Khan Academy|access-date=2016-11-06}}</ref>