# 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.