Free Fall Formula: Definition, Solved Examples

Content Curator

Freefall is a common type of motion that everyone can see in their everyday lives.When an object is at rest, it has energy stored in it; when the thing begins to move, it is said to be in motion. We may see the motion of something we accidently drop. It will have a modest speed at the start, increase speed until the end, and then reach its maximum speed before colliding. There are numerous elements that influence the speed of an object in free fall.

Also read: Equations of Motion

Table of Content

Free Fall Concept
Free Fall Formula
Things to Remember
Sample Questions

Key Terms: Free fall, motion, speed, gravity, velocity, height, time, acceleration

Free Fall Concept

[Click Here for Sample Questions]

A free-falling object is one that is falling only due to impact of gravity. When a fruit ripens, for example, the earth's gravitational attraction pulls it away from the tree. The fruit that has been removed from the tree then falls to the ground in a free fall. "In a state of free fall" refers to any item that is moving and being affected solely by gravity. A downward acceleration of 9.8 ms^-2 is experienced by such an object.

Note that If the item is solely influenced by gravity, its acceleration value will always be 9.8 ms-2, whether it is falling or climbing towards its peak. So, in free fall, 'a' always equals 'g,' according to the free-fall acceleration formula. Consider an object body falling freely from a height ‘h’ with a final velocity ‘v’ for ‘t’ seconds due to gravity ‘g’. It will move according to the following equations:

Motion of Object under free fall

Variation of acceleration with time

Variation of acceleration with time

Variation of velocity with time

Variation of velocity with time

Variation of distance with time

Variation of distance with time

Free Fall Formula

[Click Here for Sample Questions]

Free fall formula is v²= 2gh. v=gt. Free Fall Equations of Motion are specified below:

First Law of Motion

Because the object's starting velocity in free fall is 0 m/sec and the acceleration acted upon is gravity's acceleration (g= 9.8 m/sec²), The equation will be

v=u+ at

u=0m/sec, a= g= 9.8 m/sec²

v= gt

The Second Law of Motion

S = ut+ 1/2(at²)

S = H, u=0m/sec, a= g= 9.8 m/sec²

H = 1/2(gt²)

Also read: Newton’s second law of motion

Motion's third equation

v2 = u2+ 2aS

S= H, u=0m/sec, a= g= 9.8m/sec²

v² = 2gH, the third equation of motion in free fall.

Also read: Newton’s third law of motion

Where,

h height travelled

v final velocity

g acceleration due to gravity

t time taken

Things to Remember

[Click Here for Sample Questions]

A state of free fall is defined as an object that is only affected by the force of gravity.
Air resistance doesn't really exist for free-falling objects.
On Earth, all free-falling objects accelerate at a velocity of 9.8 m/s/s.
Since objects are pulled towards the centre of the earth,the acceleration of free-falling objects is called the acceleration due to gravity,
In free fall, a body travels an orbit in which the total of gravitational and inertial forces is zero.

Sample Questions

Ques. Calculate the height of a body with a mass of 2 kg that falls to the earth after 5 seconds. [3 marks]

Ans. The following parameters are provided:

t = 5 seconds

We need to figure out how tall we are. As a result, we can use the first equation as shown above.

e.g., h=12gt2

By substituting the values, we get

h= 12gt2

h= 12 x 9.8 x 52

h= 4.9 x 25.

h = 122.5 m

Ques.Cotton falls after 3 seconds and iron after 5 seconds. Which is moving at a faster rate? [2 marks]

Ans. In free fall, velocity is independent of mass.

V (iron velocity) = gt = 9.8 m/s2 x 5s = 49 m/s

V (Cotton Velocity) = gt = 9.8 m/s2 x 3s = 29.4 m/s

Hence, Iron has a higher velocity than cotton.

Ques. You're on the edge of a precipice when you drop a ball. The time it takes to hit the ground is 10 seconds.[4 marks]

Ans. 1) How high do you stand?

You already know that gravity is 9.8 m/s2 and the time is 10 seconds.

h = 1/2 gt2

h = 1/2 (9.8 m/s2) X (10 sec)2

h = 490 m

2) What was the ball's velocity?

You already know that gravity is 9.8 m/s2 and time is 10 seconds.

v = gt

v = 9.8 m/s2 x 10 sec

v = 98 m/s

Ques. When a ball is dropped from a specific height and takes 10 seconds to reach the ground, what is the final velocity of the ball? There is no consideration for air resistance. [take g=10 m/sec2] [2 marks]

Ans.Using the first equation of motion in free fall

u= 0m/sec, S=H, a= g= 10 m/sec2, (given)

v= u+ at

v= gt

v= 10 x 10

v= 100m/sec

Ques. Rohan threw his ball from a height of 5 meters and then dashed downstairs to see if he could grab it; it took him one minute to get to the ground. Will he be able to catch the ball? Note that air friction is not taken into account. [3 marks]

Ans. Using the second equation of motion in free fall,

S= ut+ 1/2(at2)

u=0 m/sec, a= g= 9.8 m/sec2, S=H

H= 1/2(gt2)

5= 1/2(9.8 t2)

t2= 10/9.8

t= 1.01 second,

As can be seen, Rohan takes an entire minute to reach the ground, whilst the ball takes only 1.01 seconds.Hence, he will be unable to catch the ball.

Ques. What will be the velocity of an object on the 10th second if it is in free fall?

Ans. Under free fall, the first equation of motion is applied. [2 marks]

v= gt

v= 9.8 x 10

v = 98 m/s

As a result, the object's velocity on the 10th second will be 98m/sec.

Ques. Find the height at which a toy is dropped if it is in free fall and the toy's ultimate velocity is 20 meters per second. [3 marks]

Ans. Using the third equation of motion.

v2= u2+ 2aS

Under free fall,

u= 0m/sec, a= g= 9.8m/sec2, S=H

v2= 2gH

202 = 2 x 9.8 x H

400 = 19.6 x H

H = 20.40 meters

Ques. Assume that a free-fall attraction at an amusement park begins at rest and then drops. After 2.3s, what is the speed of the ride? During the 2.3-s time span, how far do participants on the ride fall? [4 marks]

Ans. Let the positive direction be upward.

Vf = Vi + at

= (0 m/s)+(-9.8 m/s2)(2.3 s)

=-23 m/s

=23 m/s downwards

Where xi = 0 m and vi = 0 m/s,

xf =1/2 at2 = 1/2(-9.8 m/s2)(2.3 s2)

= -26 m

During the 2.3-s time span, the people fell 26 meters.

Ques.Why do we sometimes feel weightless? Is it determined by the center of gravity? [3 marks]

Ans. When there is no force to support your body, you will experience weightlessness. The support you feel from the floor, the seat, and other surfaces gives you a sense of weight. Weightlessness occurs if your body loses contact with these supports or is in free fall. The center of gravity is the location at which the body's weight is thought to act. The sensation of being weightless has nothing to do with the location of one's center of gravity.

Also Read:

Speed and Velocity	Difference Between Centre of Gravity and Centroid	Aristotle Fallacy	Moving Charges and Magnetism
Weightlessness	Value of G on Moon	Unit of Speed	Unit of Momentum
Earth Satellites	Photoelectric Effect	Optical Density	Some Natural Phenomena due to Sunlight
Particle Nature of Light	Einstein's Photoelectric Equation	Relative Speed	Average Acceleration Formula
Frames of Reference	Sliding Friction	Kinematics Equation	Distance and Displacement

Free Fall Formula: Definition, Solved Examples

Free Fall Concept

Motion of Object under free fall

Free Fall Formula

First Law of Motion

The Second Law of Motion

Motion's third equation

Things to Remember

Sample Questions

CBSE CLASS XII Related Questions

1.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

2.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

3.
What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

4.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

5.
Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

6.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

Comments

SUBSCRIBE TO OUR NEWS LETTER

Free Fall Formula: Definition, Solved Examples

Free Fall Concept

Motion of Object under free fall

Free Fall Formula

First Law of Motion

The Second Law of Motion

Motion's third equation

Things to Remember

Sample Questions

CBSE CLASS XII Related Questions

1.Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

2.Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

3.What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

4.A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

5.Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

6.Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

2.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

3.
What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

4.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

5.
Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

6.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.