SOLUTION: A 500 N force is used to lift a 100 N box and the box has a change of KE equal to 2000 J. How high was the box lifted?

Let "h" be the height the box lifted (the unknown quantity under the problem's question).


The mass of the box is   = 10 kilograms  (here 10 in the denominator represents the gravity acceleration of 10 m/s^2).


The work done by the force  F = 500 N  is  A = F*h = 500*h  joules.


Its part of 2000 J was spent to change the kinetic energy (KE).


The rest of the job, 500h - 2000 was spent to change the potential energy mgh.


So, we write this equation

    500h - 2000 = 10*10*h,

or

    500h - 2000 = 100h

    500h - 100h = 2000

       400h     = 2000

           h     =  = 5 meters.


ANSWER.  The box was lifted 5 meters up.