Calculating Velocity of Meteor Rock Fragment Falling on Neptune

[Avis]

Homework Statement

A 1250kg meteor rock fragment is momentarily at rest at an altitude of 3000km above the surface of Neptune. Neptune has a mass of 1.03x10²⁶kg and a radius of 2.48x10⁷m.

Determine: how much work is done on the rock by Neptunes Force of gravity as the rock falls to Neptunes surface (I got the answer to this one it was 3.74x10¹⁰J

I need help on: the velocity with which the rock strikes Neptunes surface

Not sure where to start with this one.

 

[joseg707]

If you can find the gravity on Neptune, you can use conservation of energy to determine it's velocity.

 

[Avis]

so:
W=Ek
3.74x10^10j=1/2mv^2
3.74x10^10j=1/2(1250kg)v^2
v= (square root of) 3.74x10^10j/1250kg
= 7.7X10^4

But the answer says 7.7X10^3

Where did i go wrong?

 

[joseg707]

The 1/2 magically disappeared. :) You just forgot to multiply by 2, but you got essentially.

 

[Avis]

i screwd up there... when i take half of the 1250kg i get the answer above.