Understanding the Distance Traveled by a Free-Falling Body

Free-falling bodies are a fundamental concept in physics, often used in educational settings to demonstrate basic principles of motion under gravity. This article explores the calculation of the distance traveled by a body that falls freely under the influence of gravity, utilizing the provided data and assumptions.

Given Data and Assumptions

Consider a freely falling body that travels 72 meters in 6 seconds. We assume the body starts from rest.

Determining the Acceleration Due to Gravity

The formula for the distance traveled under constant acceleration is:

s -0.5 g t^2

Given:

s -72 meters t 6 seconds g acceleration due to gravity

Substituting the given values:

-72 -0.5 g (6^2)

Solving for g:

-72 -0.5 g (36)

g -72 / 18 -4 m/s^2

Significance of Negative Gravity

Note that the negative sign indicates a direction, meaning the acceleration is downward, which is the standard convention in physics. For simplicity, we will use the magnitude of 4 m/s^2.

Calculating Distance for 3 Seconds

Two approaches are presented:

Approach 1: Initial 3 Seconds

Using the newly found value of g 4 m/s^2 and the formula for distance:

s -0.5 g t^2

Substituting t 3 seconds:

s -0.5 (4) (3^2) -0.5 (4) (9) -18 meters

The negative sign indicates the direction, so the body falls 18 meters in 3 seconds, starting from rest.

Approach 2: Total 9 Seconds

If the question is asking for the total distance traveled in 9 seconds:

s -0.5 (4) (9^2) -0.5 (4) (81) -162 meters

The increase in distance traveled from 6 seconds to 9 seconds is:

162 - 72 90 meters

Alternative Scenarios

The problem does not explicitly state the scenario for the 3 seconds. Possible interpretations include:

Distance traveled in the next 3 seconds after the initial 3 seconds. Distance traveled in the first 3 seconds of the 6-second period. Distance traveled in a 3-second period after an unspecified time of falling under gravity.

Without further clarification, we should consider the most straightforward interpretation, which is calculating the distance for the initial 3 seconds.

Conclusion

The distance traveled by a freely falling body in 3 seconds, starting from rest, is 18 meters. If the question implies a different scenario, it is essential to clarify the context. Understanding these basic principles helps in solving more complex problems involving free-falling bodies and gravity.

References:

Gravity on Mercury: -3.7 m/s^2 Gravity on Mars: -3.71 m/s^2