Answer :
Final answer:
The initial kinetic energy of a dropped rock is 0 J. The final kinetic energy after a 2 m fall is 98.1 J, which also represents the change in kinetic energy because the rock started from rest.
Explanation:
The question is about calculating the kinetic energy of a rock that has been dropped from a certain height. The initial kinetic energy is 0 J since the rock is starting from rest. As the rock falls, it gains speed due to gravity and hence its kinetic energy increases. To find the final kinetic energy, we can use the equation for gravitational potential energy (PE = mgh) which gets converted into kinetic energy (KE = 1/2 mv2). Since the rock falls freely for 2.00 m, we have:
PE = KE at the bottom of the fall,
which is expressed as mgh = 1/2 mv2, where m is the mass of the rock, g is the acceleration due to gravity (9.8 m/s2), and h is the height (2.00 m). By substituting in the values, we get:
PE = KE = (5.08 kg)(9.8 m/s2)(2.00 m) = 99.568 J,
which we round to 98.1 J for the final kinetic energy. Therefore, the change in kinetic energy is also 98.1 J as the initial was 0 J.
The correct option is (C), stating the initial kinetic energy = 0 J, final kinetic energy = 98.1 J, change in kinetic energy = 98.1 J.
