If a monkey drops a banana off a cliff where are the potential and kinetic energies of the banana equal
A quarter of the way down
At the bottom
At the top
Half way down
The potential energy of an object is at its maximum when it is at the highest point, and the kinetic energy is at its maximum when it is at the lowest point. As the banana falls, the potential energy decreases and the kinetic energy increases.
Therefore, the potential and kinetic energies of the banana are equal at the bottom of the cliff.
The potential energy of an object is defined as its energy due to its position or height above the ground relative to a reference point. The kinetic energy of an object is the energy it has due to its motion.
When the banana is at the top of the cliff, it has the maximum potential energy as it is at the highest point relative to the reference point (the ground). As the banana falls, it starts converting its potential energy into kinetic energy.
At any point during the fall, the sum of the potential energy and the kinetic energy will be equal to the initial potential energy when the banana was at the top of the cliff. Therefore, the potential and kinetic energies of the banana will be equal at the bottom of the cliff, where the banana has zero potential energy (as it has reached the ground) and the maximum kinetic energy (as it is moving at its fastest).
So, the potential and kinetic energies of the banana are equal at the bottom of the cliff.
To determine where the potential and kinetic energies of the banana are equal, we need to understand the principles of potential energy and kinetic energy.
Potential energy refers to the energy possessed by an object due to its position or state. In the case of the falling banana, potential energy is directly related to its height above the ground. As the banana falls, its potential energy decreases.
Kinetic energy, on the other hand, is the energy possessed by an object in motion. It is directly related to the object's velocity. As the banana falls, its velocity increases, and therefore its kinetic energy also increases.
Now, let's consider the options you've provided:
1. A quarter of the way down: At this point, the banana has fallen some distance but is still relatively high above the ground. Since it has not reached the bottom yet, its potential energy is still relatively high. However, its velocity and kinetic energy are not yet at their maximum.
2. At the bottom: When the banana reaches the bottom, its potential energy is at its lowest point since it is closest to the ground. At the same time, its velocity and kinetic energy reach their maximum, as it is moving with its highest speed.
3. At the top: When the banana is at the top of the cliff, it has not yet fallen and has maximum potential energy. Its velocity and kinetic energy are both zero since it is stationary.
4. Halfway down: At this point, the banana has fallen halfway between the top and bottom. Its potential energy has decreased by half since it has fallen halfway, and its velocity and kinetic energy have increased, but they are not yet at their maximum.
Based on the principles above, the potential and kinetic energies of the banana are equal at the bottom of the cliff. This is because, at this point, the potential energy is at its minimum (zero) and the kinetic energy is at its maximum.
Therefore, the answer to your question is: The potential and kinetic energies of the banana are equal at the bottom of the cliff.