Displacement in Conversation of Energy on Incline vs Projectile

[logan3]

How come when I do a conservation of energy up an incline the displacement is the distance up the incline, but when I do a conservation of energy from a projectile the displacement is not the resultant of the x and y displacements (instead, it's only the displacement in the y-direction)?

Thank-you

 

[A.T.]

If the forces are only along y, then only y-displacement matters for work done. Look up the definition of work and of the dot product involved in it.