## Gravitation Question

1. The problem statement, all variables and given/known data

A meteorite which is travelling directly towards the centre of Jupiter, has a velocity of magnitude vi =1.00 x 104 m/s when it is at a very great distance from Jupiter. At the instant of collission with the surface of Jupiter, it has a velocity of magnitude vf. Calculate vf.

Universal constant of gravitation G = 6.67 x 10-11

Radius of Jupiter = 7.15 x 107m

Mass of Jupiter = 1.90 x 1027kg

2. Relevant equations

Potential Energy (Ep)= $$\frac{-GMm}{r}$$

Kinetic Energy (Ek) = $$\frac{GMm}{2r}$$

Kinetic Energy (Ek) = $$\frac{1}{2}$$ mv2

3. The attempt at a solution

I assume that since the meteorite is at such "a great distance" it is not affected by the gravitational pull of Jupiter. Therefore its potential energy at that point must be zero.

I thought that due to conservation of energy:

Ek1 + Ep1 = Ek2 + Ep2

Ek1 & Ep1 being the Total energy at the great distance.

And

Ek2 + Ep2 being the Total energy at the instant of collission.

Therefore:

$$\frac{1}{2}$$ x m x (1 x 104)2 + 0 = $$\frac{1}{2}$$ mv2 + $$\frac{-GMm}{r}$$

Now this is where I got stuck. I don't have m, the mass of the meteorite, so I don't know what to do at this point. I would appreciate any help/clues/tips at all.

Thank you,
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 Recognitions: Homework Help m can be canceled from both the sides.

 Quote by rl.bhat m can be canceled from both the sides.
But I only have one m on the left and 2 on the right?

Recognitions:
Homework Help

## Gravitation Question

 Quote by UnoTesticulo But I only have one m on the left and 2 on the right?
You can take m common from right and cancel with m from left.

 Quote by rl.bhat You can take m common from right and cancel with m from left.
Oh ok, thank you :)

 Tags gravitation, jupiter, kinetic energy, meteorite, potential energy