My Notes You push a box of mass 24 kg with your car up to an icy hill slope of irregular shape to a height 5.7 m. The box has a speed 12.1 m/s when it starts up the hill, the same time that you brake. It then rises up to the top (with no friction) with a horizontal velocity before immediately falling off a sheer cliff to the ground (with no drag). (a) What is the speed of the box at the top of the hill?

The speed of the box at the top of the hill will be 5.693m/s.

Explanation:

The kinetic energy of the box at the bottom of the hill is

putting in and   we get

Now, the potential energy this box gains as it rises up the hill is

Therefore, the energy left in the box at the top if the hill will be

This left-over energy must appear as the kinetic energy of the box at the top of the hill (where else could it go? ); therefore,

putting in numbers and solving for we get:

Thus, the speed of the box at the top of the hill is 5.693m/s.