Work Done by F on a Ball: Path or Displacement?

[wolovemm]

the question is what is the work done by F on the ball
so this is what i did
since F is constant we can apply

and now here's my question, does the work done in this case depends on the path (curve) or the displacement (straight line)?

 

[wolovemm]

so I'm trying to find the work done by F on the ball

and this is what i got

where
sqrt(2LH) is the displacement from the bottom to the position with height H.

So, I'm just wondering if this is correct or I'm missing something

 

[Doc Al]

and now here's my question, does the work done in this case depends on the path (curve) or the displacement (straight line)?

It depends on the component of the displacement in the direction of the force. (Read up on the meaning of the scalar/dot product of two vectors.)

 

[vijay123]

it depenson dsplacement...kinectic converted into gravitational