Question
A student drops a basketball into a pool from a height of 5 meters
Answers
Answered by
GPT-4o mini
When a basketball is dropped into a pool from a height of 5 meters, a couple of physical principles come into play, namely gravity and fluid dynamics.
### Key Points to Consider:
1. **Free Fall**: When the basketball is released from rest, it will fall freely under the influence of gravity. The gravitational acceleration (\(g\)) is approximately \(9.81 \, \text{m/s}^2\).
2. **Time of Fall**: The time (\(t\)) it takes for the basketball to reach the surface of the water can be calculated using the equation of motion for free fall:
\[
h = \frac{1}{2} g t^2
\]
Rearranging gives:
\[
t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 5 \, \text{m}}{9.81 \, \text{m/s}^2}} \approx \sqrt{1.02} \approx 1.01 \, \text{s}
\]
3. **Impact with Water**: When the basketball enters the water, it will experience a sudden change in resistance from the water, causing it to decelerate rapidly. The effect of buoyancy will also act on it, which depends on the volume and density of the basketball versus that of the water.
4. **Submersion and Floating**: The basketball is likely to float due to its buoyancy, unless it is waterlogged or has a significant amount of water entering it.
5. **Dynamics after Impact**: The behavior of the basketball after it hits the water will depend on its properties (density, volume, shape) and the properties of the water (viscosity, density).
6. **Further Considerations**: If analyzing the entire scenario (like performing calculations for how long it stays submerged or how high it bounces after hitting the water), additional data about the basketball's material properties and dimensions would be needed.
Overall, the basketball will fall, impact the water surface, and float due to buoyant forces if it remains intact.
### Key Points to Consider:
1. **Free Fall**: When the basketball is released from rest, it will fall freely under the influence of gravity. The gravitational acceleration (\(g\)) is approximately \(9.81 \, \text{m/s}^2\).
2. **Time of Fall**: The time (\(t\)) it takes for the basketball to reach the surface of the water can be calculated using the equation of motion for free fall:
\[
h = \frac{1}{2} g t^2
\]
Rearranging gives:
\[
t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 5 \, \text{m}}{9.81 \, \text{m/s}^2}} \approx \sqrt{1.02} \approx 1.01 \, \text{s}
\]
3. **Impact with Water**: When the basketball enters the water, it will experience a sudden change in resistance from the water, causing it to decelerate rapidly. The effect of buoyancy will also act on it, which depends on the volume and density of the basketball versus that of the water.
4. **Submersion and Floating**: The basketball is likely to float due to its buoyancy, unless it is waterlogged or has a significant amount of water entering it.
5. **Dynamics after Impact**: The behavior of the basketball after it hits the water will depend on its properties (density, volume, shape) and the properties of the water (viscosity, density).
6. **Further Considerations**: If analyzing the entire scenario (like performing calculations for how long it stays submerged or how high it bounces after hitting the water), additional data about the basketball's material properties and dimensions would be needed.
Overall, the basketball will fall, impact the water surface, and float due to buoyant forces if it remains intact.