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Free Fall Formula

Freefall is a common kind of motion which everybody can observe in daily life. If we drop something accidentally we can see its motion. In the beginning, it will have low speed and until the end, it gains speed and before the collision, it reaches its maximum speed. Many factors are there to affect the speed of the object while it is in free fall. We deal with such free-fall motion and free fall formula with examples in this article. Let us learn the concept!

Free Fall Formula

Concept 

Freefall refers to a situation in physics where the only force acting on an object is gravity and hence acceleration due to gravity. Freefall as its term says is a body falling freely because of the gravitational pull of the earth. This motion will have the effect of acceleration due to gravity. This type of motion will follow the three equations of motion under gravity.

Projectile motion is another important category of free-fall problems. Although these events unfold in the three-dimensional world, for basic physics purposes, they are considered as two-dimensional on paper.

A very unique but interesting property of the acceleration due to gravity is that it is the same for all masses. This was far from the self-evident fact, until the days of Galileo Galilei. That was because in reality gravity is not the only force acting as an object falls, and the effects of air resistance tend to cause lighter objects to accelerate more slowly. It is something that we have all noticed when comparing the fall rate of a rock and a feather.

Galileo conducted this ingenious experiments at the “leaning” Tower of Pisa and proving by dropping masses of different weights from the top of the tower that gravitational acceleration is independent of the mass of the objects.

Free-fall physics problems are having the assumption of the absence of air resistance. But, in the real world, the Earth’s atmosphere provides some resistance to an object in free fall. Also, particles in the air collide with the falling object, which results in transforming some of its kinetic energy into thermal energy. This results in “less motion” or a more slowly increasing downward velocity.

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The formula for free fall:

Imagine an object body is falling freely for time t seconds, with final velocity v, from a height h, due to gravity g. It will follow the following equations of motion as:

  1. h= \( \frac{1}{2}gt^2 \)
  2. v²= 2gh
  3. v=gt

Where,

h Height traveled
v Final velocity
g Acceleration due to gravity
t Time taken

These equations can be derived from the usual equations of motions as given below, by substituting

initial velocity u=0,

distance traveled s=h and

acceleration, a=g.

We can see it as follows:

s= \( ut+ \frac{1}{2}at^2\)

v² =u²+ 2as

v=u+at

Freefall is the autonomous phenomena of the body with some mass. It only depends on height from the surface and the time period for which the body is flung.

Solved examples:

Example-1: Compute the height of the body if it has a mass of 2 Kg and touches the ground after 5 seconds?

Solution:

Given parameters are:

Time t = 5 sec

We have to compute the height. So, we can apply the first equation as given above.

i.e. h=  \( \frac{1}{2}gt^2 \)

Substituting the values,

h= \( \frac{1}{2}gt^2 \)

h=  \( \frac{1}{2}\times 9.8 \times 5^2 \)

h= 4.9 × 25

h = 122.5 m

Therefore height as required will be 122.5 meter.

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