Disregarding Air Resistance, What Is The Speed Of A Ball Dropped From 12 Feet Just Before It Hits The Ground?(Use $1 , \text{ft} = 0.30 , \text{m}$, And $g = 9.8 , \text{m/s}^2$.)A. 2.4 M/s 2.4 \, \text{m/s} 2.4 M/s B. $8.4 ,

Introduction

When a ball is dropped from a certain height, it accelerates downward due to the force of gravity. In this article, we will explore the physics of a falling ball and calculate its speed just before it hits the ground, disregarding air resistance. We will use the given conversion factors and the acceleration due to gravity to derive the solution.

Given Information

• The ball is dropped from a height of 12 feet.
• The conversion factor between feet and meters is given as $1 , \text{ft} = 0.30 , \text{m}$.
• The acceleration due to gravity is given as $g = 9.8 , \text{m/s}^2$.

Calculating the Initial Velocity

Since the ball is dropped from rest, its initial velocity is zero. We can represent this as:

$$v_0 = 0 \, \text{m/s}$$

Calculating the Time of Fall

The time it takes for the ball to fall from a certain height can be calculated using the equation:

$$t = \sqrt{\frac{2h}{g}}$$

where $h$ is the height from which the ball is dropped, and $g$ is the acceleration due to gravity.

Substituting the given values, we get:

$$t = \sqrt{\frac{2 \times 12 \, \text{ft} \times 0.30 \, \text{m/ft}}{9.8 \, \text{m/s}^2}}$$

Simplifying the expression, we get:

$$t = \sqrt{\frac{7.2 \, \text{m}}{9.8 \, \text{m/s}^2}}$$

$$t = \sqrt{0.735 \, \text{s}^2}$$

$$t = 0.857 \, \text{s}$$

Calculating the Speed of the Ball

The speed of the ball just before it hits the ground can be calculated using the equation:

$$v = v_0 + gt$$

Since the initial velocity is zero, the equation simplifies to:

$$v = gt$$

Substituting the values, we get:

$$v = 9.8 \, \text{m/s}^2 \times 0.857 \, \text{s}$$

$$v = 8.4 \, \text{m/s}$$

Conclusion

In this article, we calculated the speed of a ball dropped from 12 feet just before it hits the ground, disregarding air resistance. We used the given conversion factors and the acceleration due to gravity to derive the solution. The result shows that the speed of the ball is $8.4 \, \text{m/s}$.

Discussion

The result obtained in this article is consistent with the expected behavior of a falling object. The speed of the ball increases as it falls due to the acceleration due to gravity. The result also shows that the speed of the ball is independent of its initial velocity, as expected.

Limitations

The result obtained in this article assumes that air resistance is negligible. In reality, air resistance can have a significant effect on the motion of a falling object, especially at high speeds. Therefore, the result obtained in this article should be used with caution and only for situations where air resistance is negligible.

Future Work

In future work, it would be interesting to investigate the effect of air resistance on the motion of a falling object. This could involve using more complex models that take into account the forces of air resistance and friction. Such models could provide a more accurate description of the motion of a falling object and could be used to predict the behavior of objects in a variety of situations.

References

• [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics (10th ed.). John Wiley & Sons.
• [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers (10th ed.). Cengage Learning.

Appendix

The following is a list of the equations used in this article:

• $$v_0 = 0 \, \text{m/s}$$

• $$t = \sqrt{\frac{2h}{g}}$$

• $$v = v_0 + gt$$

• v = gt$<br/>

Q: What is the acceleration due to gravity?

A: The acceleration due to gravity is the rate at which an object falls towards the ground due to the force of gravity. It is denoted by the symbol $g$ and has a value of approximately $9.8 \, \text{m/s}^2$ on the surface of the Earth.

Q: How do I calculate the time it takes for an object to fall from a certain height?

A: To calculate the time it takes for an object to fall from a certain height, you can use the equation:

$$t = \sqrt{\frac{2h}{g}}$$

where $h$ is the height from which the object is dropped, and $g$ is the acceleration due to gravity.

Q: What is the relationship between the initial velocity and the final velocity of an object in free fall?

A: The initial velocity of an object in free fall is zero, and the final velocity is determined by the acceleration due to gravity. The relationship between the initial and final velocities is given by the equation:

$$v = v_0 + gt$$

where $v_0$ is the initial velocity, $g$ is the acceleration due to gravity, and $t$ is the time of fall.

Q: How do I calculate the speed of an object in free fall?

A: To calculate the speed of an object in free fall, you can use the equation:

$$v = gt$$

where $g$ is the acceleration due to gravity, and $t$ is the time of fall.

Q: What is the effect of air resistance on the motion of a falling object?

A: Air resistance can have a significant effect on the motion of a falling object, especially at high speeds. It can slow down the object and cause it to fall more slowly than it would in the absence of air resistance.

Q: How do I take into account the effect of air resistance on the motion of a falling object?

A: To take into account the effect of air resistance on the motion of a falling object, you can use more complex models that include the forces of air resistance and friction. These models can provide a more accurate description of the motion of a falling object and can be used to predict the behavior of objects in a variety of situations.

Q: What are some real-world applications of the concept of free fall?

A: The concept of free fall has many real-world applications, including:

• Calculating the time it takes for objects to fall from a certain height
• Determining the speed of objects in free fall
• Predicting the behavior of objects in a variety of situations, such as in the presence of air resistance or friction
• Designing and optimizing systems, such as parachutes or skydiving equipment

Q: What are some common misconceptions about free fall?

A: Some common misconceptions about free fall include:

• The idea that objects in free fall will eventually reach a terminal velocity and stop falling
• The idea that the speed of an object in free fall is determined by its initial velocity
• The idea that air resistance has no effect on the motion of a falling object

Q: How do I determine the terminal velocity of an object in free fall?

A: The terminal velocity of an object in free fall is the maximum speed it can reach in the presence of air resistance. It can be determined by using the equation:

$$v_t = \sqrt{\frac{2mg}{\rho A C_d}}$$

where $m$ is the mass of the object, $g$ is the acceleration due to gravity, $\rho$ is the density of the air, $A$ is the cross-sectional area of the object, and $C_d$ is the drag coefficient.

Q: What are some common applications of the concept of terminal velocity?

A: The concept of terminal velocity has many common applications, including:

• Designing and optimizing systems, such as parachutes or skydiving equipment
• Predicting the behavior of objects in a variety of situations, such as in the presence of air resistance or friction
• Calculating the time it takes for objects to fall from a certain height
• Determining the speed of objects in free fall