Final answer:
The mass of the first pebble m1 is greater than the mass of the second pebble m2 because it must have the same kinetic energy after falling from half the height compared to the second pebble. The correct answer is m1 > m2.
Step-by-step explanation:
When comparing two pebbles of masses m1 and m2 dropped from heights h and 2h, respectively, and each hitting the floor with the same kinetic energy K, we must consider the relationship between gravitational potential energy and kinetic energy. The kinetic energy K a pebble has upon reaching the floor represents the amount of potential energy it has lost during its fall. Since potential energy (PE) is given by PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height from which it was dropped, we know that the kinetic energy upon impact for pebble 1 is m1gh and for pebble 2 is m2g(2h) = 2m2gh.
For the kinetic energies to be equal, K = m1gh must equal K = 2m2gh. This implies m1 must be twice the mass of m2 to have the same kinetic energy after falling from twice the height. Therefore, the correct relationship between the masses of the pebbles is m1 > m2.