Final answer:
To find the kinetic energy of a rock falling from rest through 15 meters before hitting water, use the conservation of energy principle to equate the initial potential energy to the kinetic energy just before impact and solve for velocity and kinetic energy.
Step-by-step explanation:
To calculate the kinetic energy of a rock falling from rest through a distance of 15 meters before it hits the water, you can use the energy conservation principle. Assuming air resistance is negligible, all the potential energy is converted to kinetic energy. When the rock is at rest, it has maximum potential energy and no kinetic energy. As it falls, this potential energy is gradually converted to kinetic energy.
The potential energy (PE) of the rock at the height of 15 meters is given by PE = mgh, where m is the mass of the rock, g is the acceleration due to gravity (9.81 m/s2), and h is the height from which the rock is dropped. The kinetic energy (KE) of the rock just before impact can be found using KE = 1/2 m v2, where v is the velocity of the rock at impact. To find v, you can use the equation derived from the conservation of energy: mgh = 1/2 m v2.
After canceling the mass (m) from both sides, you use the height (15m) and gravity (9.81 m/s2) to solve for v. Once you have v, you can then calculate KE = 1/2 m v2 to find the kinetic energy at impact.