Final answer:
The diver will have a kinetic energy of 7500 J just before hitting the water, as all the gravitational potential energy will have been converted into kinetic energy, assuming no energy losses.
Step-by-step explanation:
The student asked how much kinetic energy a diver will have just before hitting the water, given that they have a gravitational potential energy of 7500 J while standing on a 10m platform. In the absence of air resistance and other external forces, the conservation of energy principle states that the total mechanical energy of the diver remains constant throughout the dive. Therefore, the gravitational potential energy the diver has at the top will be converted into kinetic energy as they fall.
The gravitational potential energy (PE) is calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the reference point. Just before the diver hits the water, all of this potential energy will have been converted into kinetic energy (KE), assuming no energy is lost to air resistance or other forces. Therefore, the kinetic energy of the diver just before impact will be equal to their initial potential energy, which is 7500 J.
This concept is similar to the calculation of the change in gravitational potential energy as a truck goes downhill. For instance, the change in potential energy is calculated as Mgh, where M is the mass of the truck, leading to a calculation for a certain scenario (Mgh = (10,000 kg) (9.80 m/s²) (75.0 m) = 7.35 × 10⁶ J). In both cases, the potential energy is being converted into kinetic energy as the system loses height.