An object with a mass of 500 kg is dropped from a tall crane. after having fallen 70 % of the total distance to the ground, the object has a potential energy of 44100 joules. what is its kinetic energy at this time?

102900 Joules

Explanation:

Assuming the kinetic energy was zero at the moment of release, you can make the following argument to solve the problem:

The potential energy at full height was mgh. We are told that after 70% of the distance, i.e., mg(0.3h) = 44.1kJ. Since potential energy is linear in altitude h, we get get the full potential energy to be 44.1kJ/0.3. The difference between full potential energy and the one after 70% of the way must equal the gained kinetic energy (neglecting stuff like heat due to friction). So,

44.1kJ/0.3 - 44.1kJ = 0.7*44.1kJ/0.3 = 102.9kJ = Ekinetic

The kinetic energy after 70% of the falling distance was 102.9 kJ.