Physics

We can calculate the final momentum of the block at the bottom of the incline using the work-energy principle.

 

Kinetic Energy and Work Done:

The initial kinetic energy of the block is .

As the block slides down the frictionless incline, the gravitational force does work on it. The work done by gravity as the block moves a distance along the incline is:

 

where is the vertical displacement of the block.

 

Total Kinetic Energy:

The total kinetic energy of the block when it reaches the bottom of the incline is the sum of its initial kinetic energy and the work done by gravity:

 

Final Velocity:

The final velocity can be found from the kinetic energy:

 

Setting the two expressions for total kinetic energy equal: