List of Projectile Motion Formula

What is Projectile Motion:

Todays we are going to learn projectile motion formula 

Projectile motion is a motion experienced by an object when thrown in the space that is moves along a curved path under the action of gravity only

When we throw some objects in space, it takes a curved path. And then it falls down due to gravity. That objects also known as Projectile

When we throw some objects in space, it possess both horizontal motion and vertical motion. There is acceleration in the vertical direction, the velocity in the horizontal direction is constant.

How ? lets prove it.

List of projectile motion formula 

• Displacement 

Ok , lets see example of basketball.

when we throw basketball in air,  that ball performs both horizontal motion and vertical motion

Horizontal motion is toward the x axis, and vertical motion is toward y axis.

The horizontal displacement performed by basketball is 

X=Vo tcosθ

The vertical displacement performed by basketball is 

Y= V0 tsin(𝜭)- 1/2 gt2

Acceleration:

In projectile motion, there is only acceleration in the vertical direction. So acceleration in the horizontal direction or x axis is constant.

Let's take again example of basketball , 

when we throw a ball, acceleration in the horizontal direction is constant.

due to gravity , acceleration of ball is changes in vertical direction

So acceleration in x axis and y axis is 

ax  =0

ay  =-g

Velocity

We know that velocity is equal to displacement divided by time

V=X/t

Where X is displacement , and t is time.

Again consider when we throw basketball in air, it possess both horizontal velocity and vertical velocity

The horizontal velocity performed by basketball A is 

Vx= V0 COS (𝜭)

Vo is the initial velocity 

Θ is the angle at which objects are thrown into the air.

The Vertical velocity performed by basketball is 

Vy= V0 SIN (𝜭)-gt

Time of flight:

The total time t for which an object or projectile remains in the air is called the time of flight..

We know vertical displacement is 

Y= V0 tsin(𝜭)- 1/2 gt2

When an object or projectile comes to the ground or x axis, then displacement y becomes zero

0= V0 tsin(𝜭)- 1/2 gt2

After rearranging above equation we get 

t=2V0sin(𝜭)/g

This is the equation of time of flight

If angle of projection Θ =0

Then sinΘ=0

Then above equation becomes t=0

Means If angle of projection is minimum then time of flight is also minimum 

Maximum Height of projectile:

When we throw a ball at a certain angle 𝜭, it will reach a certain height where velocity will be zero.

That height where Vy=0 is known as maximum height of projectile

We know that , The Vertical velocity performed by ball is 

Vy= V0 SIN (𝜭)-gt

At maximum height Vy=0.

Vy= V0 SIN (𝜭)-gt

0=V0 SIN (𝜭)-gt

So therefore 

th=V0 SIN (𝜭)/g

This is time to reach maximum height

For the vertical displacement of the maximum height of projectile:

H=V0 tsin(𝜭)- 1/2 gt2

If we put equation of th in above equation

H= V02 sin2 𝜭/2g

This is equation of Maximum Height of projectile:

In the above equation height H is directly proportional to velocity .

Mean if velocity is maximum, then Height of projectile will achieve maximum height.

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List of example of Projectile Motion:

• Basketball
• motion of football
• motion of water fountain, etc

Source

https://en.wikipedia.org/wiki/Projectile_motion