Acup sits on a table. due to its position, the potential energy of the cup is 3.00 joules. ignoring frictional effects, if the cup falls off the table, how much kinetic energy will it have when it is halfway to the floor?

If no energy is lost to friction, then ALL of the potential energy
it loses on the way down gets changed to kinetic energy.

Potential energy is just (mass)·(gravity)·(height).

The mass and gravity don't change on the way down.  The only thing
that changes is the cup's height.  When it's half way down from the table
to the floor, half of its potential energy has changed into kinetic energy.

If it had 3 Joules of potential energy on the table, then it'll have
(1/2 of 3) = 1.5 joules of kinetic energy when it's half way to the floor.

The answer should be a.