Gravitational potential

http://books.google.co.uk/books?id=CTVEAgAAQBAJ&pg=PA54&lpg=PA54&dq=2.5kg+rock+charon+pluto+speed+help&source=bl&ots=5ntOicqFIZ&sig=aMu9AhhojRUt3WxzcOiKXk7Bzfw&hl=en&sa=X&ei=BwdlU6G8OOiV0AWA7IHQCA&ved=0CC8Q6AEwAA#v=onepage&q=2.5kg%20rock%20charon%20pluto%20speed%20help&f=false

Question 17. c) i. on that link

I got the potential energy of the object from the graph (on Charon due to pluto) as 7.42x10^7 J (2.5*29.67x10^6). I then converted this to a velocity using Ek=Ep but my answer of 7702 m/s is incorrect (book answer is 935 m/s).

Could someone please explain what I have done wrong and what I should be doing

Thanks

That question isn't about Pluto and Charon. Do you mean Qu 10?

You need the potential difference between the surface of Pluto and the top of the curve. That is converted then to kinetic energy.

Sorry yes in my book its Q 17!

Could you please talk me through that, why aren't we taking into account its original potential? Also using a larger potential is going to give a larger value for Ep and therefore a larger value for Ek (my value is already 7 times too big)?

The speed it hits the surface of Pluto with will be the result of losing all its GPE falling from the top of the curve to the surface of Pluto assuming it had no KE to start with (to give the minimum speed on hitting the surface).

Your value of 2.5 x -29.67 x 10⁶ J gives the GPE at the top. (Maximum height above the planet surface.
On the surface of Pluto the GPE is 2.5 x -30 x 10⁶ J from the graph.

What is the loss of GPE?
This converts to KE.

So we are saying the rock has enough Ek to get to the peak of the graph and then this change of Ep is converted to Ek? Got it.

Can you explain the second part ii. too, I'm not sure :/

Well if you throw the rock instead from Pluto to Charon, assuming you get it to the top of the curve (you would need to throw it a lot harder to get it there from Pluto than you did from Charon) then it doesn't lose so much GPE falling from the top to the surface of Charon. It's the same calculation but with the GPE on the surface of Charon instead of Pluto.