Help with final velocity of a rocket

In summary, the problem presents the task of calculating the final velocity of a rocket given the velocity of the ejected gas, the initial mass of the rocket, and the final mass. The solution involves using the conservation of momentum principle to write an equation with the velocity of the gas as a constant, and then finding the function of velocity with respect to the changing mass.
  • #1
PhysicsLoop
4
0

Homework Statement


Calculate the final velocity of a rocket if the velocity of the ejected gas is c, initial mass of rocket is M0 and final mass is Mr, v0=0.


Homework Equations


We have to calculate the final velocity of rocket.


The Attempt at a Solution


Because the total momentum of an isolated system is conserved, the total system - rocket + exhausted gas - must still have zero momentum.
If the velocity of gas is c, then:
M0*v - (M0-m)*c=0
m - mass of gas ejected

What to do next?
 
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  • #2
Welcome to PF!

Hi PhysicsLoop! Welcome to PF! :smile:
PhysicsLoop said:
Because the total momentum of an isolated system is conserved, the total system - rocket + exhausted gas - must still have zero momentum.

Ah, but you don't know what the final velocity of the gas is (it changes according to the velocity of the rocket at the time).

You'll need to write a differential equation for what happens when the speed is v and the mass is m, and a small amount of mass dm is ejected. :wink:
 
  • #3
Thanks! :)
Velocity of the gas is constant equal with c (speed light), it doesn't change with rocket velocity.
Can you help me? I'm stucked.
 
  • #4
v is a function of m

write the equation for conservation of momentum when the mass changes from m to m - dm
 
  • #5
I still don't get it... Can you write it please?
 
  • #6
Can someone help me with this?
 

1. What is the final velocity of a rocket?

The final velocity of a rocket refers to the speed at which the rocket is traveling at the end of its journey. It is the result of the acceleration and time of the rocket's flight.

2. How is the final velocity of a rocket calculated?

The final velocity of a rocket can be calculated by using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

3. What factors affect the final velocity of a rocket?

The final velocity of a rocket is affected by factors such as the thrust of the rocket, the mass of the rocket, and the resistance of the air or other external forces acting on the rocket.

4. Can the final velocity of a rocket be increased?

Yes, the final velocity of a rocket can be increased by increasing the thrust of the rocket, reducing its mass, or minimizing external forces acting on it. This can be achieved through various engineering and design techniques.

5. How does the final velocity of a rocket impact its flight?

The final velocity of a rocket plays a crucial role in determining the success of its flight. A higher final velocity allows the rocket to reach greater distances and heights, while a lower final velocity may result in a shorter flight or even failure to reach its intended destination.

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