Calculating Work Done by Air Resistance on a Thrown Ball

[Elysium]

Hi, I'm having problems with this question:

2. A 0.63-kg ball is thrown straight up into the air with an initial speed of 14 m/s. It reaches a height of 8.1 m, then falls back down. Assume that the only forces acting are those of gravity and air resistance and calculate the work done during the ascent by the force of air resistance. (Hint: Use the CWE theorem and the potential energy associated with the gravitational work.)

ok first I determined what work that gravtity does which is m*g*(delta y) which in this case is -50 J

I then used the CEW theorem equation using the velocities to find the total work done: (sigma W) = 1/2 m (v^2 (final) - v^2(initial)) which is -62 J

Last part is that I used the relationship between the work of gravity and the total work (sigma)W = W of gravity + Work of air resistance. I got -12 Joules for air resistance. I don't know but I feel like I got something wrong here. Can anyone help me out?

 

[verty]

Well, the difference between the kinetic energy at the bottom and the potential energy at the top will be the amount lost due to air resistance.

E_a = (1/2)mv^2 - mgh = 61.7 - 50
= 11.7J

W_a = E_a
= 11.7J

I don't know the method you have used.

Edit: Work is a scalar I see.