Finding the Interval of Time Taken

Oct 13, 2025 by pynkocean.com 94 views

Introduction

In physics, the study of motion is a fundamental concept that helps us understand how objects move and interact with their environment. One of the most basic types of motion is free fall, where an object is dropped from a certain height and falls towards the ground under the sole influence of gravity. In this article, we will explore the concept of an object being dropped from a small plane and use the given formula to find the interval of time taken for the object to reach the ground.

The Formula for Distance

The distance, $d$ , above the ground after $t$ seconds, is given by the formula $d = -16t^2 + 1,000$ . This formula represents a quadratic equation, where the coefficient of the $t^2$ term is negative, indicating that the distance decreases as time increases.

Understanding the Formula

To understand the formula, let's break it down into its components. The term $-16t^2$ represents the effect of gravity on the object, where the negative sign indicates that the distance decreases as time increases. The term $1,000$ represents the initial height of the object above the ground.

Finding the Interval of Time Taken

To find the interval of time taken for the object to reach the ground, we need to find the values of $t$ that satisfy the inequality $d \geq 0$ . This is because the distance above the ground cannot be negative, so we need to find the values of $t$ that make the distance greater than or equal to zero.

Solving the Inequality

To solve the inequality, we need to isolate the term $t^2$ on one side of the equation. We can do this by subtracting $1,000$ from both sides of the inequality:

-16t^2 + 1,000 \geq 0

Subtracting $1,000$ from both sides gives us:

-16t^2 \geq -1,000

Dividing both sides by $-16$ gives us:

t^2 \leq 62.5

Taking the square root of both sides gives us:

t \leq \sqrt{62.5}

Finding the Interval of Time Taken

Now that we have found the values of $t$ that satisfy the inequality, we can find the interval of time taken for the object to reach the ground. The interval of time taken is given by the range of values of $t$ that satisfy the inequality.

The Interval of Time Taken

The interval of time taken for the object to reach the ground is given by:

0 \leq t \leq \sqrt{62.5}

This means that the object will reach the ground in a time interval of $0$ to $\sqrt{62.5}$ seconds.

Conclusion

In this article, we used the given formula to find the interval of time taken for an object to reach the ground after being dropped from a small plane. We solved the inequality $d \geq 0$ to find the values of $t$ that satisfy the condition, and then found the interval of time taken for the object to reach the ground. The interval of time taken is given by $0 \leq t \leq \sqrt{62.5}$ seconds.

References

[1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
[2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.

Additional Resources

[1] Khan Academy. (n.d.). Free Fall. Retrieved from https://www.khanacademy.org/science/physics/one-dimensional-motion/one-dimensional-motion-problems/v/free-fall
[2] Physics Classroom. (n.d.). Free Fall. Retrieved from https://www.physicsclassroom.com/class/1DKin/Lesson-1/Free-Fall

Discussion

What do you think about the concept of free fall? Have you ever experienced a situation where you felt like you were in free fall? Share your thoughts and experiences in the comments below!

Introduction

In our previous article, we explored the concept of an object being dropped from a small plane and used the given formula to find the interval of time taken for the object to reach the ground. In this article, we will answer some of the most frequently asked questions related to this topic.

Q: What is the formula for distance above the ground?

A: The formula for distance above the ground is given by $d = -16t^2 + 1,000$ , where $d$ is the distance above the ground and $t$ is the time in seconds.

Q: What is the significance of the negative sign in the formula?

A: The negative sign in the formula indicates that the distance above the ground decreases as time increases. This is because the object is falling under the sole influence of gravity.

Q: How do I find the interval of time taken for the object to reach the ground?

A: To find the interval of time taken for the object to reach the ground, you need to solve the inequality $d \geq 0$ . This will give you the values of $t$ that satisfy the condition, and you can then find the interval of time taken.

Q: What is the interval of time taken for the object to reach the ground?

A: The interval of time taken for the object to reach the ground is given by $0 \leq t \leq \sqrt{62.5}$ seconds.

Q: What is the significance of the square root of 62.5 in the interval of time taken?

A: The square root of 62.5 represents the maximum time it takes for the object to reach the ground. This is because the object will reach the ground in a time interval of $0$ to $\sqrt{62.5}$ seconds.

Q: Can I use this formula to find the distance above the ground at any given time?

A: Yes, you can use this formula to find the distance above the ground at any given time. Simply plug in the value of $t$ into the formula and solve for $d$ .

Q: What are some real-world applications of this concept?

A: This concept has many real-world applications, such as:

Calculating the time it takes for an object to fall from a certain height
Determining the distance an object will travel under the influence of gravity
Understanding the motion of objects in free fall

Q: Can I use this concept to solve other problems related to motion?

A: Yes, you can use this concept to solve other problems related to motion. For example, you can use it to calculate the time it takes for an object to reach a certain velocity or to determine the distance an object will travel under the influence of a constant acceleration.

Conclusion

In this article, we answered some of the most frequently asked questions related to the concept of an object being dropped from a small plane. We hope this article has been helpful in clarifying any doubts you may have had about this topic.

References

[1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
[2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.

Additional Resources

[1] Khan Academy. (n.d.). Free Fall. Retrieved from https://www.khanacademy.org/science/physics/one-dimensional-motion/one-dimensional-motion-problems/v/free-fall
[2] Physics Classroom. (n.d.). Free Fall. Retrieved from https://www.physicsclassroom.com/class/1DKin/Lesson-1/Free-Fall

Discussion

Do you have any questions about this concept? Share your thoughts and experiences in the comments below!