**Free Fall Formula**

**Introduction: **

Free fall refers to the motion of an object under the sole influence of gravity, without any other forces acting on it. In free fall, all objects experience the same acceleration due to gravity (g), which is approximately 9.8 m/s² near the surface of the Earth. This acceleration acts downwards, towards the center of the Earth.

**Formula for Free Fall: **

The formula for calculating the distance (d) traveled by an object in free fall is given by:

d = (1/2) x g x t²

where: d represents the distance or height fallen, g is the acceleration due to gravity, and t is the time of fall.

The formula can be rearranged to solve for other quantities. For example:

- To calculate the time of fall (t): t = √(2d/g)
- To calculate the final velocity (v) at the end of free fall: v = gt

**Meaning of Variables:**

- Distance (d): It represents the vertical distance traveled by the falling object. The unit of distance can be meters (m) or any other suitable unit of length.

- Acceleration due to Gravity (g): It is the constant acceleration experienced by objects in free fall due to the gravitational force. The unit of acceleration is meters per second squared (m/s²).
- Time (t): It refers to the duration of the free fall, measured in seconds (s).

**Assumptions for Free Fall: **

The formula for free fall assumes that the object starts from rest (initial velocity u = 0) and is only influenced by the gravitational force. It neglects factors such as air resistance, the rotation of the Earth, and the variation of gravity with altitude.

Consistent units need to be applied when applying the formula and consider the direction of motion (positive or negative) based on the chosen reference frame.

**Applications of Free Fall Formula: **

The free fall formula is often used to calculate the distance fallen or the time of fall for objects dropped or thrown vertically. It helps determine the vertical motion of objects in scenarios such as objects falling from a height, projectiles launched vertically, or bodies dropped into a well.

Understanding the free fall formula allows us to analyze and predict the motion of objects in the absence of other forces, providing valuable insights into various physical phenomena and practical applications.

**Solved Examples on Free Fall Formula:**

**Example 1:** A stone is dropped from a tall building. How far does it fall in 3 seconds?

Solution:

Given:

Time of fall (t) = 3 seconds.

Using the free fall formula: d = (1/2) x g x t²

Substituting the given values: d = (1/2) x 9.8 x (3)²

d = 4.9 x 9

d = 44.1 meters

Therefore, the stone falls approximately 44.1 meters in 3 seconds.

**Example 2: **An object is released from rest and falls freely for 2 seconds. What is its final velocity?

Solution:

Given:

Time of fall (t) = 2 seconds

Acceleration due to gravity (g) = 9.8 m/s².

Using the free fall formula to calculate the distance fallen: d = (1/2)x g x t²

Substituting the given values:

d = (1/2) x 9.8 x (2)²

d = 4.9 x 4

d = 19.6 meters

Now, we can calculate the final velocity (v) using the formula:

v = gt

Substituting the value of g and t:

v = 9.8 x 2

v = 19.6 m/s

Therefore, the final velocity of the object after 2 seconds of free fall is 19.6 m/s.

**Example 3:** A ball is dropped from a height of 25 meters. How long does it take to reach the ground?

Solution:

Given:

Distance fallen (d) = 25 meters,

Acceleration due to gravity (g) = 9.8 m/s².

Using the free fall formula: d = (1/2) x g x t²

Rearranging the formula to solve for time (t): t² = (2d) / g

t = √((2d) / g)

Substituting the given values:

t = √((2 x 25) / 9.8)

t ≈ √(50 / 9.8)

t ≈ √5.1

t ≈ 2.26 seconds

Therefore, it takes approximately 2.26 seconds for the ball to reach the ground when dropped from a height of 25 meters.

**Frequently Asked Questions on Free Fall Formula:**

1: What is the formula for free fall?

Answer: The formula for free fall is: h = (1/2)gt², where h is the height fallen, g is the acceleration due to gravity, and t is the time elapsed.

2: What is free fall?

Answer: Free fall refers to the motion of an object when it is solely under the influence of gravity, experiencing no other forces such as air resistance or propulsion. In free fall, an object is subjected to a constant acceleration due to gravity, which is approximately 9.8 m/s² near the Earth’s surface. As a result, the object falls towards the ground with increasing velocity until it reaches its terminal velocity or hits the ground, depending on the circumstances.

3: Why is it called free fall?

Answer: It is called “free fall” because it refers to the motion of an object falling solely under the influence of gravity, without any other forces acting upon it. During free fall, the object is not supported or propelled by any external factors, allowing it to move freely and solely in response to gravity.

4: Does free fall depend on mass?

Answer: No, free fall does not depend on mass. In the absence of air resistance, all objects, regardless of their mass, will experience the same acceleration due to gravity. This acceleration is approximately 9.8 meters per second squared on Earth. Therefore, during free fall, objects of different masses will fall with the same acceleration and follow the same path, neglecting any effects of air resistance or other external forces. This principle was famously demonstrated by Galileo Galilei with his “thought experiment” involving different masses dropped from the Leaning Tower of Pisa.

5: Why is acceleration in free fall constant?

Answer: The acceleration due to gravity during a free fall is constant because the force of gravity experienced by an object is primarily determined by the mass of the Earth and the distance between the object and the Earth’s center. Near the surface of the Earth, the distance remains relatively constant for most practical purposes, resulting in a consistent gravitational force. According to Newton’s second law of motion, this constant force leads to a constant acceleration for any object in free fall, regardless of its mass. Therefore, the acceleration due to gravity remains constant during free fall.

6: What factors affect free fall?

Answer: The factors that affect free fall include the acceleration due to gravity, which determines the rate of acceleration during the fall. Air resistance plays a role, especially for objects with larger surface areas or different shapes. The altitude or location can slightly impact the acceleration due to gravity. The mass and shape of the object influence factors like air resistance and terminal velocity. External forces, such as propulsion or external pushes or pulls, can alter the motion during free fall. While these factors may impact the specifics of free fall, in idealized scenarios without air resistance or significant external forces, gravity remains the dominant factor governing free fall.

7: Is free fall acceleration negative?

Answer: In most cases, the acceleration due to free fall is considered negative when using a coordinate system with upward direction defined as positive. This convention is commonly used to indicate that the object is accelerating downwards under the influence of gravity. However, it’s important to note that the magnitude of the acceleration due to free fall is always positive, which is approximately 9.8 m/s² near the Earth’s surface. The negative sign simply indicates the direction of the acceleration relative to the chosen coordinate system.

8: What is acceleration due to gravity in free fall?

Answer: The acceleration due to gravity in free fall is approximately 9.8 m/s² near the Earth’s surface. This value represents the rate at which an object’s velocity changes while it is in free fall under the influence of gravity alone. It is important to note that the actual value of acceleration due to gravity can vary slightly depending on the location and altitude on Earth, as well as other factors such as air resistance. However, 9.8 m/s² is a commonly used approximation for most practical purposes.