How high does it go?

1. Jun 5, 2009

talaroue

1. The problem statement, all variables and given/known data
A huge cannon is assembled on an airless planet. The planet has a radius of 6.00×106 m and a mass of 3.06×1024 kg. The cannon fires a projectile straight up at 5270 m/s.
An observation satellite orbits the planet at a height of 4103.30 km. What is the projectile�s speed as it passes the satellite?

2. Relevant equations
K=mv^2/2
U=-GMm/r

3. The attempt at a solution
Initially: Ki and Ui are both present
Finally: Ki and Uf are both present again
CORRECT?
so i have the equation
Ki-Ui=Kf-Uf
wanting to solve for velocity at a certain point Uf actually is GMm/(R+H)
CORRECT?
So then I solved for Vf and get .......
squareroot (2(Ki-Ui+Uf)/m)

Then i plug and go....WHY ISN'T WORKING

2. Jun 5, 2009

LowlyPion

You seem to have the basic idea.

Kinetic energy at firing + potential energy gravity at surface = potential energy at satellite + kinetic energy of projectile.

3. Jun 5, 2009

talaroue

after plugging in the KE and PE equations i came up with......-2(-.5Vi^2+GM/R-GM/(R+h))
square root of the whole thing.

4. Jun 5, 2009

talaroue

so instead of using the mass of the planet i should use mass of the sataellite?

EDIT: I don't have the mass of the satellite so I believe I have it set up right.

5. Jun 5, 2009

LowlyPion

No. Of course not.

The Mass of the Planet and G give you a way to figure your potential energy ...

U = -GM/r

So ...

at surface U = the above.
at the satellite U = -GM/(r+h)

(Don't forget the sign.)

6. Jun 5, 2009

talaroue

So then the way I set it up is right?

7. Jun 5, 2009

LowlyPion

So long as you have also accounted for the potential energy at the surface as well.

8. Jun 5, 2009

D H

Staff Emeritus
You forgot that the satellite is in orbit. It's moving, too.

9. Jun 5, 2009

talaroue

I attached my equation.

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10. Jun 5, 2009

talaroue

you can't just assume it isn't moving?

11. Jun 5, 2009

LowlyPion

I don't think they are asking for the speed relative to the satellite.

Merely the speed at the height (radius) of the satellite's orbit.

12. Jun 5, 2009

talaroue

thats what I figured. I figured that they just wanted the distance. Is my equation correct that i attached a few posts back?

13. Jun 5, 2009

LowlyPion

Looks like the - in front of the 2 is not useful.

I would examine they way you treated the mass of the projectile ... as a suggestion.

14. Jun 5, 2009

talaroue

The mass should cancel. i meant to erase it, and the 2 shouldn't be negative. I jsut worked through that equation and it said the answer is wrong.

Last edited: Jun 5, 2009
15. Jun 5, 2009

LowlyPion

Not in the equation you supplied.

16. Jun 5, 2009

talaroue

Opps that is my bad, I knew it canceled in my mind but when I re wrote it i forgot to cancel it even though I canceled the others.

EDIT: WHen i worked through it, i didn't use the negative or the mass and it was wrong

17. Jun 5, 2009

Prophet029

Has this question been resolved?

18. Jun 5, 2009

LowlyPion

Maybe show your work? Perhaps you have a simple error?

19. Jun 5, 2009

Stratosphere

Wouldn't it just be easier to use $$S(t)=-gt^{2}+V_{o}t+h_{o}$$?

20. Jun 5, 2009

D H

Staff Emeritus
No. That equation assumes a uniform gravity field.