Calculating the Distance Fallen by a Free-Falling Body in 2 Seconds

Understanding how to calculate the distance fallen by a free-falling body under the force of gravity is essential in both physics and engineering. In this article, we will explore the equation of motion for free fall and apply it to determine the height lost by a 10kg body in 2 seconds. We will cover the necessary calculations and ensure that the logic remains consistent throughout the process.

The Equation of Motion for Free Fall

The distance fallen by a free-falling body can be calculated using the formula:

h frac{1}{2} g t^2

Where:

h is the height lost, measured in meters g is the acceleration due to gravity, equal to approximately 9.81 m/s2 t is the time in seconds

Step-by-Step Calculation

Given that the time t is 2 seconds:

1. Calculate the square of the time:

2 seconds 2  4 seconds^2

2. Calculate the product of half the acceleration due to gravity and the square of the time:

(frac{1}{2} times 9.81 , text{m/s}^2  4.905 , text{m/s}^2)

3. Multiply the result from step 2 by the square of the time calculated in step 1:

4.905 , text{m/s}^2 times 4 , text{seconds}^2  19.62 , text{meters}

Thus, the height lost by the free-falling body in 2 seconds is approximately 19.62 meters.

Note: The mass of the body (10 kg in this case) does not affect the distance fallen in free fall, assuming no air resistance.

Assumptions and Clarifications

The calculation provided assumes the body starts from rest. If the body were to start with an initial velocity, the formula for the loss of height would be:

(text{Loss of height} frac{1}{2} g t^2)

Given:

g 9.8 m/s^2 Vi 0 (assuming it starts from rest) t 2 s

The simplified formula for height lost when starting from rest is:

h frac{1}{2} g t^2

Plugging in the values:

h frac{1}{2} times 9.8 , text{m/s}^2 times (2 , text{s})^2 19.6 , text{meters}

The Physics Behind Free Fall

When an object is in free fall, it accelerates downwards at a constant rate of 9.8 m/s2 due to gravity. This means that after 2 seconds, the object will be traveling at 19.6 m/s (as derived from the formula (v g times t)). However, it wasn't falling at this speed the entire time. Instead, it accelerated uniformly from 0 m/s to 19.6 m/s in 2 seconds. The average speed during this period can be calculated as:

(text{Average speed} frac{19.6 , text{m/s} 0 , text{m/s}}{2} 9.8 , text{m/s})

Multiplying the average speed by the time gives the distance covered:

(text{Distance} 9.8 , text{m/s} times 2 , text{s} 19.6 , text{meters})

This confirms that the height lost by the free-falling body in 2 seconds is indeed 19.6 meters.

Conclusion

Understanding the physics of free fall and the equation h frac{1}{2} g t^2 allows us to accurately calculate the distance that a free-falling body will cover. The mass of the object does not affect this distance, as long as air resistance is negligible. By applying these principles, we can solve similar problems with confidence.

References

Physics Classroom - Free Fall HyperPhysics - Trajectories