# Acceleration of rocket in space

1. Nov 4, 2013

### Rekrap999

I am sorry for the wall of text but i need some help with a problem in one of my classes. i am still in my semester as an engineer and this problem was given in my college acclimation class (i know it is ridiculous).

One fundamental problem in manned space travel is that the enormous distances require high
velocities to reach an intended destination in a reasonable time, and reaching large velocities also
requires large accelerations. Say you are in a spaceship that is floating in outer space at zero
velocity and no forces acting on it. If the ship’s initial mass is 10000 kgs (including you and its
fuel) and it can produce a stream of superheated gases for propulsion coming out of the ship at a
velocity of 10 km/s, use the equation for conservation of linear momentum in open systems 2
discussed in class (sum forces + rate of linear momentum in – rate of linear momentum out =
d(mv)/dt) to find:
a.- How much is the mass rate for the outlet gases that is needed to get an initial acceleration of
one standard gravity, i.e., 9.8 m/s2
?
b.- If only 1/3 of the ship’s mass can be used for fuel, and assuming the mass rate you obtained
in part a remains constant, how long will it take to exhaust the fuel?
c.- Assuming that the acceleration is maintained constant by using the constant mass rate you
calculated in part a (an assumption that does not hold true in this case), what is the velocity
obtained by the time the fuel is exhausted? Calculate the distance traveled during that time,
which for constant acceleration can be obtained as a*t
2
/2, where a is the acceleration and t is the
time.

2. Nov 4, 2013

### arildno

How is "rate of linear momentum out" related to mass ejection rate and exhaust velocity?

3. Nov 4, 2013

### Rekrap999

i believe the professor was trying to use this equation for a different example. in the other example it was a boat that had a drag of 1/5 the velocity of the boat. and you had to find out how fast it was going.

4. Nov 4, 2013

### arildno

So?
What have you learnt about the expression for the momentum flux, i.e, the rate of momentum leaving the system.

5. Nov 4, 2013

### Rekrap999

absolutely nothing. i am taking a class called the Arizona State Experience, it is a mandatory class with 20 mechanical engineering students and is taught completely by the TA. usually homework is to find a job for the major or find a research paper, never actual math until now. i am sorry i cant be more helpful.

6. Nov 4, 2013

### arildno

I don't believe you.
You have a textbook, surely?
Notes from class?

7. Nov 4, 2013

### Rekrap999

i dont have a book, it is a 1 unit class. the only example we were given was a boat. the force of drag=5*velocity of the boat, the boat weighed 10 kg, the engine moved water at a rate of 33m/s. and it was solved for the net forces on the boat.

8. Nov 4, 2013

### arildno

"use the equation for conservation of linear momentum in open systems 2 DISCUSSED in class"
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We don't give out free solutions here, with no work being done by original poster.

9. Nov 4, 2013

### Rekrap999

I am not looking for a free answer, its just that this is due in 2.5 hours and i have classes or the next 2 hours.

10. Nov 4, 2013

### arildno

11. Nov 4, 2013

### Rekrap999

no need to be a dick about me being stressed over an assignment that 10% of my grade.

12. Nov 4, 2013

### arildno

You are the one who are rude, waiting to the LAST minute before your assignment is due before demanding others to do your homework for you.
You've had all week, at least, so don't come here wailing about others, when it is your own atrocious, lazy study habits that are at fault.