Free Fall Formula

What is Free Fall Formula?

A free falling object formula describes the self-governing phenomena of the body having some mass. A free-fall concept that talks about the body freely falling under gravity. 

Assume that a body with velocity v is descending freely from a mountain of height (h) for time (t) seconds. Now, because of gravity (g), the body falls in the following manner:

                              

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From this example, we can describe the free fall motion formula. As it covers a certain distance, so we can describe the free fall distance formula. An object possessing a free fall object formula bears velocity, which we can calculate by using the free fall velocity formula.

Since the object falling from a mountain has a maximum height, so does the object. The eight can be calculated by using the maximum height formula free fall.

As there is a rate of change of velocity in an object while free-falling, so we can determine the free fall acceleration formula as well.

So, on this page, we will cover all the equations for a falling body along with the free fall physics formula, and then derive free fall formula as well.


Free Fall Physics Formula

We know that any object that is moving and being acted upon only by the force of gravity is said to be "in a state of free fall." Such an object experiences a downward acceleration of 9.8 ms-2

We must note that whether the object is falling or rising towards its peak if it is under the sole influence of gravity, its acceleration value will always remain 9.8 ms-2

So, the free fall acceleration formula says that ‘a’ always equals ‘g’ under free fall. 


Free Falling Bodies Formula

The free fall motion formula covers the following equations for a falling body:

  • Maximum height formula free fall

  • free fall velocity formula

The maximum height formula free fall is:

                  h    =   1/2 gt2

The free velocity formula is:

                    v2  =  2gh, and

                      v   =  gt

Now, let us derive free fall formula:


Free Falling Object Formula

Below are the following kinematic equations for deriving the free fall motion formula:

First equation: vf   =  vi  +  at  ………..(1)

The second equation: d  =  vi + vf/2 . t…..(2)

The third equation: vf2   =  vi2  +  2* a* d…..(3)

The fourth equation: d  =  vit +  1/2 at2…..(4)

Here, we replaced ‘s’ with ‘d’, and ‘d’ is the displacement

vand vf are the initial and the final velocities of a falling object

a = acceleration, and

t = time in seconds


Free Fall Velocity Formula

We must note that the initial velocity of the object will become zero, so the first equation becomes:

vf   =   at

Also, according to the free fall object formula, ‘a = g,’ so the equation (1) becomes:

vf   =   gt

This free falling bodies formula is the free fall velocity formula.                        

Also, from equation (3), we have:

vf2   =  vi2  +  2* a* d

Or,

vf2   =  2gh…….(5)

This is again the free fall velocity formula.

   

Free Fall Distance Formula

From equation (4), we see that displacement is the height travelled by the falling object. So substituting ‘with ‘h,’  and ‘a’ with ‘a,’ we have:

                                   h  =  vit +  1/2 at2                        

Putting vi   = 0:

                                h  =  1/2 gt2    

This is the required  free fall equation with height ‘h.’    

                         

Maximum Height Formula Free Fall

From equation (5), we have:

                        vf2   =  2gh

The maximum height formula free fall is:

                            h   =   vf2/2g


Concepts to Free Falling Objects Problem Solving

There are a few concepts of free-fall motion that hold paramount importance when using the equations to analyze free-fall motion. These concepts are as follows:

  • A freely falling object experiences an acceleration of 9.8 ms-2.  (Here, the negative sign indicates a downward acceleration or deceleration)

Whether clearly stated or not, the value of the acceleration in the kinematic equations remains 9.8 ms-2 for any freely falling object.

  • If an object is mistakenly dropped (as opposed to being thrown) from an elevated height, its initial velocity remains 0 m/s.

  • If an object is projected upwards in an exactly vertical direction, it slows down as it rises upward. The point at which it reaches the peak of its trajectory is the point where the velocity is 0 m/s. This value can be used as one of the important motion parameters in the kinematic equations; for instance, the final velocity (vf) after travelling to the peak reaches a value of 0 m/s.

  • If an object is projected upwards in an exactly vertical direction, its velocity at which it is projected equals in magnitude but in a sign opposite to the velocity after it returns to the same height. 

In the nutshell, a ball projected with an upward velocity of + 50 m/s will have a downward velocity of - 50 m/s when it returns to the same height.

Now, let’s apply these concepts in solving problems on a free fall formula:


Free Fall Formula Calculator

For understanding the free fall formula; let’s have a look at the below examples to apply the equation for freely falling body:

Example 1: What will be the height of the body height if it has a mass of 3 kg and after 8 seconds it reaches the ground?

Solution:

Given data: 

Height h =?

Time t = 8s

You are acquainted with the concept that free fall is independent of mass. So, using the free fall formula here:

h  =  1/2 gt2 

Putting g  = 9.8 ms-2 and t = 8s:

h = 1/2 *  9.8* (8)2

On solving, we get:

h = 313.6 m

Answer: Therefore, the maximum height that a body covers to reach the ground is 313.6 m.


Example 2:  The cotton ball falls after 4 s and iron ball falls after 7 s. Determine which object falls with a higher velocity?

Solution:

Since the velocity in free fall is independent of mass, so apply the following formula:       

v (Velocity of cotton ball) = gt = 9.8 m/s2 × 4 s = 39.2 m/s

v (Velocity of iron ball) = gt = 9.8 m/s2 × 7 s = 68.6 m/s

We see that the iron ball falls with a higher velocity than the cotton ball.


Conclusion

We call the free fall bodies formula the kinematic equations free fall because they are derived from kinematic equations.

Also, free fall is independent of the mass and it only depends on the height the object fell from.

FAQs (Frequently Asked Questions)

1. How Do You Calculate The Time of a Falling Object?

Ans: Firstly, measure the distance the object covered while freely falling (in feet) with a ruler or measuring tape. 

Secondly, divide the measured distance by 16. 

For instance, if the object falls from a 128 feet mountain, divide 128 by 16, we get 8. 

Now, calculating the square root of the obtained number, i.e., 8 result, we get the time it takes the object to fall in seconds.

2. What is the Law of Free Fall?

Ans: Galileo's law of free fall statement:

In the absence of air resistance (air friction), all bodies (irrespective of their mass) fall with the same acceleration. 

We must note that this law is an approximation shown by using Newtonian mechanics.

3. Write Three Examples of Free Fall.

Ans: Close to the surface of the Earth, an object that falls freely in a vacuum accelerates at 9.8 m/s2. If there is an air resistance acting on an object that has been dropped, the object eventually reaches a terminal velocity, which is around 53 m/s (190 km/h or 118 mph) for a human skydiver.