Gravitation Question

UnoTesticulo

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 v_i =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 v_f. Calculate v_f.

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 (E_p)= [tex]\frac{-GMm}{r}[/tex]

Kinetic Energy (E_k) = [tex]\frac{GMm}{2r}[/tex]

Kinetic Energy (E_k) = [tex]\frac{1}{2}[/tex] 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:

E_k1 + E_p1 = E_k2 + E_p2

E_k1 & E_p1 being the Total energy at the great distance.

And

E_k2 + E_p2 being the Total energy at the instant of collission.

Therefore:

[tex]\frac{1}{2}[/tex] x m x (1 x 10⁴)² + 0 = [tex]\frac{1}{2}[/tex] mv² + [tex]\frac{-GMm}{r}[/tex]

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,

rl.bhat

m can be canceled from both the sides.

UnoTesticulo

But I only have one m on the left and 2 on the right?

rl.bhat

You can take m common from right and cancel with m from left.

UnoTesticulo

Oh ok, thank you :)