Displacement in Conversation of Energy on Incline vs Projectile

AI Thread Summary
In conservation of energy on an incline, the displacement is measured along the incline due to the direction of the forces acting on the object. In contrast, for a projectile, only the vertical (y-direction) displacement is relevant for calculating work done, as the forces primarily act in that direction. This distinction arises from the definition of work, which involves the dot product of force and displacement vectors. Understanding the orientation of forces is crucial in determining the appropriate displacement to use in energy conservation calculations. Therefore, the context of the motion dictates how displacement is defined in energy conservation scenarios.
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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
 
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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.
 

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