How Does Dropping Rocks from Different Heights Affect Kinetic Energy Ratios?

[sugz]

Homework Statement

A rock is dropped from a distance RE above the surface of the Earth, and is observed to have a kinetic energy of K1, when it hits the ground. An identical rock is dropped from 2RE above the surface and has kinetic energy K2 when it hits the ground. Re is the radius of the earth. What is K2/K1.

a) 2 b) 4/3 c) 3/2 d) 2/3 e)4

Homework Equations

The Attempt at a Solution

K1= (-GMm)/(RE+ RE)= (−GMm)/2RE K2 = (-GMm)/(RE+ 2RE)= (−GMm)/3RE

K2/K1 = [(−GMm)/3RE]/[(−GMm)/2RE] = [(−GMm)/3RE] * [(2RE/(−GMm)] = 2/3 = d).
However the answer is 4/3, where did I go wrong?

 

[gneill]

You want to compare the changes in PE that each rock undergoes when they fall. Where does each rock end up at then end of its fall? Not at infinity...

 

[sugz]

Oh I see where I made a mistake, thank you!

 

[Sparkling Eyes]

But how do we compare the changes in PE do we do mgRe?

 

[haruspex]

But how do we compare the changes in PE do we do mgRe?

No. Those distances are too great to be taking g as a constant. Use PE_grav=-GMm/r, as in the OP.