Final answer:
The kinetic energy when the gravitational potential energy has decreased to 15 J would be 15 J, due to the conservation of mechanical energy in the absence of friction or air resistance.
Step-by-step explanation:
The question pertains to the conservation of mechanical energy in the absence of friction or air resistance. Initially, the object has a kinetic energy (KE) of 10 J and a gravitational potential energy (PE) of 20 J. When the PE decreases to 15 J, due to conservation of energy, the KE must increase by the amount the PE has decreased. This is because the decrease in PE must be offset by an equivalent increase in KE, since no energy is lost to non-conservative forces like friction.
The total initial mechanical energy is the sum of KE and PE, which is 10 J + 20 J = 30 J. If the PE decreases to 15 J, the KE must increase to maintain the total mechanical energy. Thus, the new KE will be 30 J - 15 J = 15 J.