Answer:
1,960,000 Joules
Step-by-step explanation:
To calculate the kinetic energy of an object, you can use the formula:
Kinetic Energy (KE) = 0.5 * mass * velocity^2
Given that the boulder has a mass of 200 kg, we need to determine the velocity at each given height to calculate its kinetic energy.
When the boulder is 1000 m above the ground:
At this height, the boulder is not in motion, so its velocity is 0 m/s. Therefore, the kinetic energy is:
KE = 0.5 * mass * velocity^2 = 0.5 * 200 kg * (0 m/s)^2 = 0 Joules
The kinetic energy is 0 Joules.
When the boulder has fallen 500 m:
To determine the velocity, we can use the conservation of energy principle. The potential energy lost due to the fall is converted into kinetic energy. The potential energy lost can be calculated using the formula:
Potential Energy (PE) = mass * acceleration due to gravity * height
PE = 200 kg * 9.8 m/s^2 * 500 m = 980,000 Joules
Since the potential energy is converted to kinetic energy, the kinetic energy of the boulder when it has fallen 500 m is equal to the potential energy lost:
KE = 980,000 Joules
The kinetic energy is 980,000 Joules.
Just before the boulder hits the ground:
At this point, we assume that all of the potential energy has been converted into kinetic energy. Therefore, the potential energy just before hitting the ground is equal to the kinetic energy. Using the same formula as above:
PE = mass * acceleration due to gravity * height
PE = 200 kg * 9.8 m/s^2 * 1000 m = 1,960,000 Joules
The kinetic energy just before the boulder hits the ground is 1,960,000 Joules.