Free fall is the physical name for the trajectory and speed of objects, when they are influenced only by the acceleration of gravity, which directs them downwards, based on the weight of that body. For example, when an apple falls off a table.

Important in understanding the speed at which objects fall, impacts they can cause on the ground, speed allowed during the journey, among other factors, the topic of free fall appears in questions on several national entrance exams. Study now with this Owl article!

## Concepts in free fall

Free fall occurs when any body of mass m is abandoned in the environment and follows a trajectory towards the ground, under the exclusive action of the acceleration of gravity. One of the main statements of free fall is that it is a movement that is directed always **vertical** . In other words, it can only happen in two directions: from bottom to top or from top to bottom.

Furthermore, it is important to emphasize that the displacement is only considered free fall when the only force acting on the body is the force generated by gravity **,** which is generally accepted as g = 10 m/s ^{2} .

The value of the acceleration of gravity may appear different in some tests, such as g = 9.8 m/s ^{2} . This happens because gravity is influenced by the distance between two bodies in space and some other mechanical conditions. Therefore, it is important to pay extra attention to the **values provided** by the statement.

When there is a free fall from top to bottom, like a stone falling from the top of a roof, the acceleration of gravity acts increasing the body’s speed every second. This is why **the greater the height** of a fall, **the greater the impact** suffered by the mass.

### Object downwards.

The other option is for an object to be thrown upwards, like the balls used by jugglers. The body only reaches a certain height because it loses speed as it moves through space — this situation is a consequence of the negative influence of the gravitational force, which always drives the object downwards.

After some time, the trajectory stops and the object stops in the air, falling again in the same direction as the acceleration due to gravity. This is the main concept of vertical throwing, which allows bodies to return to the ground even when thrown upwards.

Note, finally, that the definitions of free fall are completely immersed in the field of mechanics, because it studies energy, speed, acceleration, mass and other factors of displacement.

## Free fall: formulas

As we saw in the previous topic, the direction of free fall is always vertical, but the direction of movement can be either **upward** or **downward** . This difference is important to better understand the formulas of this topic.

**Gravity** is considered to have a positive direction , that is, all forces that point vertically downwards will also be considered positive. On the other hand, forces and vector quantities that have the arrow pointing up are given as negative.

With this information in hand, it is possible to apply mathematical formulas that relate time, acceleration, displacement, distance traveled and speed to provide characteristics of a free fall.

These formulas are derived from the study of Uniformly Varied Motion (MUV), after all, in the dynamic study of a free fall, the behavior observed is that of a MUV, under the action of gravity acceleration.

### Speed equation

V = gt

V = speed of fall, in m/s

g = acceleration of gravity, in m/s ^{2}

t = observed time interval, in seconds.

This equation is useful for knowing what speed a body is at during a certain point in free fall. For example, a stone that falls from a building for 7 seconds, reaches the ground at what speed?

Considering g=10m/s ^{2} , the calculation to be made must be:

- V = gt
- V = 10.7
- V = 70 m/s

### Height

The height of a free fall is closely related to how long the body will take to fall, and consequently, it is also related to the speed adopted during the journey. Therefore, there is a formula to calculate this height (H) of fall:

H = gt ^{2} /2

H = height, in meters

g = acceleration of gravity, in m/s ^{2}

t = observed time interval, in seconds.

Using the same example as in the previous topic, we can admit that the height of the building was:

H = gt ^{2} /2

H = 10 .7 ^{2} /2

SO H = 490/2

H@= 245 m

### Free fall equation: speed and height

Finally, using Torricelli’s equation, it is possible to relate the height, gravity and speed of the body in the same formula:

V2 ^{=} 2.gH

In this case, let’s confirm the experiment mentioned above, considering that we didn’t know the height of the fall:

V ^{2} = 2.gH

70 ^{2} = 2.10.H

4900 = 2.10.H

490 = 2.H

490/2 = H

AND H = 245 m

## Freefall graphics

Free fall has first and second degree formulas, so that, when it comes to the position of the body (or height of fall), the path is parabolic. On the other hand, speed is obtained in a first degree calculation, with a straight line graph.

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