# Motion Under Gravity

Last Updated : 15 Mar, 2024

Motion under gravity is the motion of an object moving under the influence of gravity. gravity is the constant pull of Earth’s surface that pulls every object to its centre. The motion of a fruit falling from the branch of the tree is considered motion under gravity.

In this article, we will learn about Motion under gravity, Equation of motion under gravity and others in detail.

## Motion Under Gravity

Gravity, described as acting by Isaac Newton, is the force that brings things with mass towards each other. Here on Earth, gravity gives an impressive force that pushes everything away from its centre, resulting in, for instance, falling objects and throwing projectiles. Understanding the nature of satellites’ motion under gravity assuming gravitational acceleration and determination of future orbits is very critical.

Motion Under Gravity

An item that experiences a change in motion which is in vertical motion due to the gravitational force is known as motion under gravity. GRAVITY is an ordinary yet powerful force which makes things move down in a free fall.

### Acceleration Due to Gravity

The gravitational acceleration is the objects’ rate at which they have been accelerating towards the Earth due to the gravitational force. Somewhere near the ground, as one approaches the Earth’s surface, this acceleration is approximately 9.8 m/s^2. The latter statement implies that in every second, what falls significantly increases its velocity by 9.8 m/s in the direction of fall. The gravitational acceleration is rather a constant value near the Earth’s surface while it may change with altitude or with the location just a bit. This is because it plays a central role in the application of this theory to diverse areas such as free fall and projectile motion.

Gravitational acceleration is typically denoted by the symbol g, and its formula is:

g = W/m

where,

• g is Gravitational Acceleration
• W is Force of Gravity Acting on Object
• m is Mass of Object

Gravitational acceleration is approximately 9.8m/s2.

## Basic Principles of Motion Under Gravity

Motion of an object under gravity is explained below in this article.

### Free Fall and Its Characteristics

Characteristics of an object under free fall is explained as:

• Free fall is motion of an object when the object is only affected by only the gravitational force, without any external force. For free fall

Acceleration = -g = -9.8 m/ss

• In free fall, acceleration of object is constant and directed always towards the Earth.
• Velocity of object under free fall increases linearly with the time.

### Effect of Gravity on Projectiles

• Projectile motion is the example of object that has the horizontal and vertical movement where the gravity effects the vertical motion of the object.
• Motion of projectile in the horizontal direction remains constant throughout the trajectory, whereas the vertical motion in projectlie motion is subject to gravitational force that consequently leads to a parabolic path.

## Equation of Motion Under Gravity

Gravitation motion equations are the results of applying the dynamic and kinematics laws. It expresses the connections between an object’s location, velocity, acceleration, and time of movement all influenced by gravity.

In free fall, an object does not experience outside forces, except for gravity. This acceleration is constant at the rate of 9.8 m/s2 toward the centre of Earth.

Displacement: Displacement ‘h’ of an object under gravity can be calculated using the equation:

h = ut + 1/2gt2

Velocity: Velocity ‘v’ of the object at any given time t can be calculated using:

v = u + gt

Final Velocity at Displacement (h): Final Velocity at Displacement ‘h’ is calculated using the equation,

v2 = u2 + 2gh

where,

• v is Final Velocity
• u is Initial Velocity
• g is Gravitational Acceleration
• h is Height of Object
• h is Height of Object

### Velocity of a Body Having Motion Under Gravity

If an object moves under the influence of gravity then its velocity is calculated as:

v2 = u2 + 2gh

Value of g is taken to be positive as it is moving downward

v2 = (0)2 + 2gh

v2 = 2gh

v = âˆš(2gh)

## Equations for Projectile Motion

Projectile motion is the motion of an object that moves under the influence gravity and also has a vrticla motion. Motion of bullet fried from a gun, motion of ball thrown in air, etc are considered as projectile motion.

Horizontal Motion: If there is no external force applied to an object, the object will keep moving with the same speed. Thus, the equation for horizontal displacement (x) is simply:

x = ut

Vertical Motion: In case of vertical motion gravity plays a crucial role, and its equation is given as,

y = ut + 1/2gt2

where sign of g can vary accordingly

Maximum Height: Maximum height (H) attained by the projectile is obtained from the formula:

H = v2sin2(Î¸)/2g

Time of Flight: Formula to find total flight time(T) is calculated by the formula:

T = 2vsin(Î¸)/g

where,

• v is Vertical Component of Initial Velocity
• Î¸ is Launch Angle
• g is Gravitational Acceleration
• x is Horizontal Displacement
• u is Horizontal Component of Initial Velocity
• t is Time

## Motion Under Gravity Forces Examples

Some examples of motion under gravity force are:

• Ballistics and Projectile Motion: Allocating shipments of food, medicine, and relief supplies to areas devastated by natural and man-made disasters
• Astronomy and Celestial Mechanics: Predicting the orbits and planning missions in space based on gravitational interactions and the law of gravity. Gravitational interactions and the law of gravity determine orbits and space missions planning.
• Engineering and Structural Design: Gravity having to be in the forefront when architects come up with such structures and space stations.
• Fluid Dynamics and Hydrodynamics: Quadratic image distributions, including ocean currents and atmospheric movements.
• Sports and Recreation: Regardless if we are talking about safe and interesting performances in paragliding and parachuting, the vital role of VR technologies is still non-replaceable.
• Geophysics and Earth Sciences: The use of gravity measurements to study the structure and in-house resources.
• Transportation and Navigation: Building transport systems that are running without loss of fuel and sturdy controls that will be used in sending vehicles and spacecraft.
• Education and Research: Through their role in physics education and research they are able to lay the theoretical foundations of physics knowledge and provide the opportunities for scientific development.

## Frequently Asked Questions Motion Under Gravity

### How does gravity affect the motion of objects in Free Fall?

In case of motion of the object in free fall the velocity of objects increases gradually.

### What are the three equations of motion under gravity?

The three equations of motion under gravity are:

• v = u + gt
• h = ut + 1/2gt2
• v2 = u2 + 2gh

### What is the second equation of motion under gravity?

First Equation of motion under gravity: v = u + gt.

### Where does the strength of gravity force maximum?

Strength of gravity is maximum at nar the Earth’s surface.

### What is the type of gravitational force?

Gravitational force is the force of attraction between Earth and other object. Earth always pushes an object.

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