Calculating Velocity of Meteor Rock Fragment Falling on Neptune

AI Thread Summary
To calculate the velocity of a meteor rock fragment falling on Neptune, the work done by Neptune's gravity was determined to be 3.74x10^10 J. Using the conservation of energy principle, the equation W = Ek was applied, leading to the formula 3.74x10^10 J = 1/2 mv^2. The correct calculation involves ensuring the factor of 2 is included, which was initially overlooked. The correct velocity upon impact is 7.7x10^3 m/s, not 7.7x10^4 m/s. Attention to detail in the calculations is crucial for accurate results.
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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.
 
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If you can find the gravity on Neptune, you can use conservation of energy to determine it's velocity.
 
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?
 
The 1/2 magically disappeared. :) You just forgot to multiply by 2, but you got essentially.
 
i screwd up there... when i take half of the 1250kg i get the answer above.
 
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