What is true about potential energy when lifting an object vertically compared to using an inclined plane?

When lifting an object vertically or using an inclined plane to raise that object, the potential energy gained by the object primarily depends on the height it is raised to, regardless of the path taken. In both scenarios, the increase in gravitational potential energy is calculated using the formula ( PE = mgh ), where ( m ) is the mass of the object, ( g ) is the acceleration due to gravity, and ( h ) is the height above a reference point.

If both methods achieve the same vertical height, the change in potential energy will be identical. This is because the vertical height is the critical factor in determining potential energy, not the distance traveled or the angle of ascent. Consequently, since both methods can elevate the object to the same elevation, the potential energy will indeed be the same in both cases, supporting the answer that both methods have the same potential energy if the height is the same.

The other choices do not accurately reflect the principles of potential energy as they suggest that the path or angle affects the potential energy without addressing that only the final height matters when calculating gravitational potential energy.