2 March 2024

Each of the laws of physics are well structured thanks to applied sciences and all the contributions that scientists have made throughout human history. That is why we can understand very well what is the science behind the free fall of a body. Of course, this simple movement is influenced by the gravity of a planet like Earth or another body that possesses gravity. In any case, we will shortly provide you with more detailed information about the movement in free fall that we consider important and necessary.

## What is free fall?

Free fall formulas are mathematical equations in which magnitudes such as speed, distance, acceleration, gravity and other variables such as height, initial and final speed are taken into account. It is thanks to the basis or science behind the free fall formulasthat we can understand how a body behaves in space, whether empty or with gravity.

Now, the key points that define free fall and its formula are the following:

• Free fall is a consequence of gravity and its effect on a body.
• Every body in free fall has an initial and final velocity and an acceleration.
• Free fall time depends on gravity, speed and height at which a body is.
• The physics behind the aerodynamic resistance is a factor that can influence the movement in free fall.
• It is possible to make a free fall calculation as long as you have all the other independent variables.
• All objects will fall towards the center of the earth.
• It is necessary to calculate the time it takes for an object to fall and this can be accomplished using one of the formulas related to the subject of free fall.
• The principles of free fall can be applied both to the field of engineering, linear algebra, as well as in physics and astrophysics.

It is important to mention that this is just one of the different types of accelerated uniform rectilinear motion. The other is the vertical launch, which is related to the free fall. In case you’re wondering what this is like, imagine you throw a ball as hard as you can into the air. This could be a vertical movementbut at a certain point, it will become a free falling object.

## Free fall and vertical launch features

Now that you know what free fall is, it’s time to move on to the features. Among all the most outstanding, we can mention the following:

1. Any body or object that is thrown vertically or is allowed to fall freely always moves in a straight line.
2. This object will have a constant acceleration of 9.8 m/s2. This belongs to the acceleration of the earth’s gravity, so it is unique in our solar system.
3. The acceleration of a freely falling body is represented by a vector pointing downward.
4. Every free fall has an initial velocity 0.
5. Any body in free fall will reach its final speed after a while in motion.
6. If an object is thrown vertically upwards, both the rise and fall times are exactly the same.
7. No matter what the mass of the bodies, they will all fall at the same speed if they are dropped or thrown from the same height.
8. If a body is thrown upwards, mathematically or physically the magnitude is represented by a negative signsince it goes against the gravity of the earth.

In theory, these are all the characteristics of the free fall of an object. However, only those from vertically accelerated uniform rectilinear motion. This means that new characteristics arise when there are variations in the angle of the trajectory of a body, star or object.

## Free fall trajectory

Regarding the last mentioned, this is where we will explain in more detail. Due to different environmental factors, the trajectory of a projectile, object or body never follow a completely straight path. This only applies to ideal cases, however, the reality is different, since there are factors such as friction, the angle at which the object leaves, the friction of the projectile with the wind, among other factors. Of course, all this taking into account that the object is thrown, now, when it is released from a resting state, the following variants arise.

### Totally vertical free fall

In this case, there are some factors that must be taken into account if it is intended to study totally vertical free fall. Among these are:

• The height at which the object is located.
• The time it will take for it to depart from its resting state, to the final ground or surface.
• The acceleration caused by the earth’s gravity.
• What is your final position.
• What is its final velocity, taking into account its zero initial velocity.

Each of these parameters has a particular magnitude. In general, you usually work with measurements such as the meter, seconds, meters per second squared, kilometers per hour, among others.

This kind of movement It is characterized by having a speed increasing, that is, it starts from zero and increases until it reaches the maximum or final speed. It is important to note that this factor in a certain way depends on the height at which the object is located. Since, if you are not high enough, you will not be able to reach the maximum speed.

From its base equation, other much more complex equations can be deduced in which factors such as the drag coefficientthe cross-sectional area, the friction of the object with some fluid, among others.

### Parabolic and quasi-parabolic free fall

As its own name indicates, they are movements that comply with the shape of a perfect parabola or an almost parabola. But what is the difference between one and the other? It all boils down to the angle of departure and the shape generated by the moving object in free fall. To know if it is a free fall in a straight or parabolic line, it is necessary to take into account if it starts from a resting state or not. If we are in the presence of the second case, the trajectory takes the form of a parabola.

Regarding the calculation of this parameter, gravity, height, speed, friction, among others, are taken into consideration. Now, as for the semi-parabolic motion, this arises as a result of friction with fluids. This taking into account that both air, water or liquids are fluids, since they have volume. This simple parameter greatly influences the trajectory that the object to be released will have in free fall. Of course, in the latter case, the equation changes a bit and the calculations are a bit different because of a new parameter.

### Free fall from great heights

This is basically the same as the first type of free fall we talked about, however, something funny happens and it all depends on the height. The higher the altitude, we can say that there is a greater probability that the trajectory change drastically. That is to say, if we drop an object at a great height, it will begin to have a straight trajectory, however, due to friction, the weight of the object, air currents and other factors influence in such a way that the trajectory in certain moment it will cease to be straight.

## Free Fall Examples

A very simple example is standing on the top floor of a building and dropping any object, be it an action figure, a rubber ball, a coin, among others. This may not reach top speedalthough everything depends on the dimensions of the object or body to be dropped and if it starts from a state at rest or if it is already accelerated.

For example, if you hold a ball and just let it go, you are starting from rest. However, when you throw it vertically down, it gains an initial velocity, so it won’t be zero, but will have a value depending on how fast you throw it.

If we go to a much more practical case, the drops of water that are generated in the rain or even hail are a clear example of this. Now, if we go to a more extreme case, the stars, asteroids or a space shuttle that falls towards the earth counts as an example of free fall. Of course, they are objects that They already have a defined initial speed and that they will be affected positively or negatively as the case may be.

## Free fall and vertical launch formulas

It is time for you to know what are the formulas used to calculate the free fall of an object. Keep in mind that you won’t always have all the parameters, so you have to do some additional calculations based on of the variables that you have and do not have.

### Formula to find height

To calculate this variable, it is necessary to differentiate whether it is free fall or flat. In any case, you have the following equation.

### Formula to find the initial velocity

In general, the initial velocity is always zero, as long as the body in free fall starts from rest. However, this will not always be the case, since we may be in the presence of a vertical launch. In such a case, you can use the following equation:

From that equation, all you have to do is clear the initial velocity variable and then clear the power of two that it has in the form of a square root and that’s it.

### Formula to find the final velocity

In the previous section you have the equation of the final speed. As long as you have all the values ​​for the calculation, in the end you may or may not take the square root of the resulting magnitude.

### formula to find time

You can find time in different ways, that is, you can start from the equation of gravity or from the height. Everything will depend on what variables you have and know their value. The equation is the following:

### formula to find gravity

The only thing left to tell you is that the formula for gravity is as follows: