Question
A player throws a baseball straight up so that the ball rises and then falls back down to the player’s hand. Which of the following changes will occur if the player throws the ball up higher and then catches it?
A. The ball will have more potential energy than kinetic energy when it is half-way back down to the player’s hand.
B. The ball will have greater potential energy at the top of its path.
C. The ball will have more kinetic energy than potential energy when it is half-way back down to the player’s hand.
D. The ball will have greater kinetic energy at the top of its path.
A. The ball will have more potential energy than kinetic energy when it is half-way back down to the player’s hand.
B. The ball will have greater potential energy at the top of its path.
C. The ball will have more kinetic energy than potential energy when it is half-way back down to the player’s hand.
D. The ball will have greater kinetic energy at the top of its path.
Answers
GPT-4o mini
To analyze the situation, we can consider the relationship between kinetic energy and potential energy in the context of throwing a baseball straight up.
1. **Potential Energy (PE)** is highest at the peak height of the ball's trajectory, where the ball momentarily comes to a stop before falling back down. The potential energy is given by the formula \(PE = mgh\), where \(m\) is mass, \(g\) is acceleration due to gravity, and \(h\) is height.
2. **Kinetic Energy (KE)** is highest just after the ball is thrown (when it's moving fastest) and lowest at the peak (when it is momentarily at rest).
Now, let's evaluate each option given the scenario that the player throws the ball higher.
A. **The ball will have more potential energy than kinetic energy when it is half-way back down to the player’s hand.**
- At half the way down, potential energy and kinetic energy are both significant. The ball's speed is increasing, so it is unlikely that potential energy would dominate at this point. This statement is likely false.
B. **The ball will have greater potential energy at the top of its path.**
- This statement would be true because throwing the ball higher means it reaches a greater height, resulting in greater potential energy at the top of its trajectory compared to when thrown lower.
C. **The ball will have more kinetic energy than potential energy when it is half-way back down to the player’s hand.**
- At halfway down, especially if it has only been thrown a little higher, for most cases, the kinetic energy will still not surpass the potential energy just yet, as it has to convert a significant amount of potential energy to kinetic energy before it retains this inequality. This one is likely false.
D. **The ball will have greater kinetic energy at the top of its path.**
- This statement is false because at the peak, the ball has maximum potential energy and minimum kinetic energy (which is zero momentarily).
In summary, the correct answer is **B. The ball will have greater potential energy at the top of its path.**
1. **Potential Energy (PE)** is highest at the peak height of the ball's trajectory, where the ball momentarily comes to a stop before falling back down. The potential energy is given by the formula \(PE = mgh\), where \(m\) is mass, \(g\) is acceleration due to gravity, and \(h\) is height.
2. **Kinetic Energy (KE)** is highest just after the ball is thrown (when it's moving fastest) and lowest at the peak (when it is momentarily at rest).
Now, let's evaluate each option given the scenario that the player throws the ball higher.
A. **The ball will have more potential energy than kinetic energy when it is half-way back down to the player’s hand.**
- At half the way down, potential energy and kinetic energy are both significant. The ball's speed is increasing, so it is unlikely that potential energy would dominate at this point. This statement is likely false.
B. **The ball will have greater potential energy at the top of its path.**
- This statement would be true because throwing the ball higher means it reaches a greater height, resulting in greater potential energy at the top of its trajectory compared to when thrown lower.
C. **The ball will have more kinetic energy than potential energy when it is half-way back down to the player’s hand.**
- At halfway down, especially if it has only been thrown a little higher, for most cases, the kinetic energy will still not surpass the potential energy just yet, as it has to convert a significant amount of potential energy to kinetic energy before it retains this inequality. This one is likely false.
D. **The ball will have greater kinetic energy at the top of its path.**
- This statement is false because at the peak, the ball has maximum potential energy and minimum kinetic energy (which is zero momentarily).
In summary, the correct answer is **B. The ball will have greater potential energy at the top of its path.**