Is my solution for a gravitational problem correct?

[WeiLoong]

Homework Statement

A stationary object is released from a point P at distance 4R from the centre of the Earth which has radius R and mas M.What is the speed of the object when it hits the Earth's surfacehttps://scontent-kul1-1.xx.fbcdn.net/hphotos-xpt1/v/t34.0-12/11921921_10204785254702789_1979507807_n.jpg?oh=4a62967277ee876cb2de85befad6b89a&oe=55E68D61

Homework Equations

Gravitational

The Attempt at a Solution

By using the principle of conservational of energy.
1/2mv^2=-GMm/R-(-GMm/4R)
which is the final point-initial point

but the solution is
1/2mv^2=-GMm/4R-(-GMm/R)
which is the initial point-final point

So which 1 is correct i got little bit confused here.Arent we should use the final-initial to find the changes of gravitatinal potential energy?

 

[BvU]

Hello,

The kinetic energy is positive. Potential energy is negative, so the book solution is correct. The energy balance you want to solve for is:

$E_{\rm kin, final } + E_{\rm potential, final} = E_{\rm kin, initial } + E_{\rm potential, initial}$ with $E_{\rm kin, initial } = 0$. If you write that out, which one do you get ?

 

[WeiLoong]

Hi, thank you for your explanation
another thing that confused me is this question

The figure below shows a point P which at a distance R from the centre of the Earth, has gravitational potential of -6kJ kg^-1 . What is the change in gravitational potential energy when a 1kg mass is moved from point P to point Q, 2R away from the centre of the earth?
https://scontent-kul1-1.xx.fbcdn.net/hphotos-xtp1/v/t34.0-12/11922950_10204785470108174_1313158553_n.jpg?oh=f63e57fca18f483818a21a849bed979c&oe=55E67634

So Gravitational potential energy at point Q is -3kJkg^-1
The change in gravitational potential energy is P-Q or Q-P. I get really confused here. since the question above use Inital - final, so i should use gravitational in point P- point Q also?

 

[BvU]

Better to write down an expression for the ratio of these energies...

Sorry, too fast. Does the potential energy become less negative ? That is the same as saying it increases, so the difference is positive.

And in the question above you did not use initial - final but initial = final. See the expression $E_{...}$

 

[WeiLoong]

Owh so the second question is using final - initial to find up the change?
-3-(-6)=+3 ?

correct me if i did mistake :D
by the way thanks for answer i truthly appreciate

 

[BvU]

No need for correction. You are doing fine !