Rocket Performance Homework: Max Velocity & Altitude

[Theboob651]

Homework Statement

I need to find out the rockets max velocity and max altitude. My teacher gave us an example but everytime i use the stuff we know his answer doesn't match mine.
So we know: Rockets mass=23 grams
mass of engine=16.2 grams
mass of propellant=3.12
average thrust=8 Newtons
burn duration=.5 seconds
His max velocity=101.37
His max altitude=549.621

Homework Equations

The equations he gave us are:
x = Xo + vt, v=Vo +at, x = Xo+Vot+.5at^2, and f=ma

x=distance, v=velocity, t=time, a=acceleration, f=force

The Attempt at a Solution

Whenever i plug all the stuff in i come up with a Max velocity of 102.04
Then i really don't know where to go from there to even check his altitude.
Please help
thanks

 

[tony873004]

Your teacher made a mistake.

Your initial mass is Mass of Rocket + Mass of Engine + Mass of propellent
Your mass is not constant. It decreases from initial mass to initial mass minus propellent mass. So find your average mass and use that for mass in the formulas you give. Your teacher's velocity of 101.37 is what I get if I forget to include propellant mass into total initial mass. I get a velocity in the low 90s if I remember to include it. I'll let you figure out the exact number.

Your average acceleration is given in your final formula, rewriting f=ma as a=f/m, where m is your average mass. That's your upward acceleration from the rocket's thrust. Your total acceleration will be this minus gravity. Your 2nd equation is v=at (since Vo is 0). Use it once you have your average acceleration.

For height, you need to break it up into two problems: 1 while the rocket is thrusting you use your average acceleration computed earlier, and 1 while the rocket is coasting to its maximum height, where acceleration will simply be 9.8 m/s down.

 

[Theboob651]

the initial mass is the rocket mass plus the engine mass, the propellant mass is included in the engine mass. the propellant mass is used to find the mass of the coasting rocket. thanks though. if you have any other ideas please help

 

[tony873004]

If that's the case then I get the same answer as your teacher. During the thrust phase, your mass begins as (rocket mass + engine mass) and ends as (rocket mass + engine mass - propellant mass). So your average mass will be halfway inbetween these values. Acceleration due to thrust = F/m, where F is 8 N, and m is the average mass you just computed. Subtract from this acceleration the acceleration due to gravity. Then use your kinematics formula and you'll get 101.369926 m/s, same as the teacher's rounded number.

 

[Theboob651]

Thanks