Students appearing for **JEE main advanced **exam must prepare themselves thoroughly to secure a seat in any of the Indian Institutes of Technology (IITs). There is a vast amount of syllabus to be covered in the upcoming months. Students must sort out the subjects and topics by the marking scheme for each topic. All three subjects – Physics, Chemistry and Mathematics require an equal amount of time for preparation. However, it also depends on the extent of one’s preparation and their strong and weak areas.

Kinematics is one of the most important areas in Physics that a student must master thoroughly. The equations will come in handy throughout the entire year when they are studying physics, or even mathematics (vectors) for the matter of fact.

Below is a short and simple wrap-up of projectile motion in Physics, that carries a good weight in the **JEE main advanced** exam.

**What is a Projectile?**

A projectile is a body (object) that is thrown into the space which is in flight and only gravity acts on it.

**What is Projectile Motion?**

Projectile motion is a form of motion that is experienced by an object that makes it move along a curved path due to the action of gravity. It is motion where the only force acting upon the object (projectile) is gravity. Also, when an object is in flight after being thrown, it is said to be in projectile motion.

** Example** –A cricket ball or a javelin in the air.

**What are the assumptions considered for Projectile Motion?**

For projectile motion, the following assumptions are considered:

- The effect on the projectile is negligible due to the curvature of the Earth
- The impact on the projectile is insignificant due to the rotation of the Earth
- There is no resistance due to air

Projectile motion has two simultaneous independent rectilinear motions:

- Along x-axis (Responsible for the horizontal motion of the object; uniform velocity)
- Along y-axis (Responsible for the vertical motion of the object; uniform downward acceleration ‘g’)

**Equations of Motion for Constant Acceleration**

The most commonly used equations for motion of an object with constant acceleration are:

*v = u – gt**s = ut – ½ gt*^{2}*v*^{2}= u^{2}– 2 gs

Here:

*u = initial velocity**g = acceleration due to gravity**t = time**s = displacement**v = final velocity*

**Equations for Projectile Motion**

If a projectile is launched with velocity *‘u’*, it makes an angle *‘θ’* with x-axis. Once the projectile is in the air, the acceleration acting on it due to gravity is directed vertically downwards:

a= -g (combined)

a_{x} = 0 __A__

a_{y} = -g __B__

Initial velocity *‘u’ *is:

u_{x} = ucosθ __C__

u_{y} = usinθ __D__

x and y = 0, if initial position is the origin of the projectile

At any time *‘t’*, displacement will be:

x = (u_{x})t = (ucosθ)t

y = (usinθ)t – (½)gt^{2 }__E__

Velocity at time ‘*t’*can be obtained by:

u_{x} = ucosθ

u_{y} = usinθ– gt __F__

The relation between ‘x’ and ‘y’ can be further explained by:

y= (tanθ)x – gx^{2}/ (4u^{2}cos^{2}θ) __G__

**Note: ***‘x’* remains constant throughout the motion, and only ‘*y*’component changes.

**Time of Flight**

In equation G, the total time t_{f}during the flight can be calculated by using y = 0. It means there is zero displacement in the vertical direction.

t_{f} = 2usinθ/g __H__

t_{f} is the time of the flight of the concerned projectile.

t_{f} = 2t_{m}(t_{m} is the time taken to reach maximum height)

**Maximum Height**

h_{max} = (u^{2}sin^{2}θ)/2g

The maximum height h_{m}can be calculated by substituting t = t_{m}

**Range**** of the Projectile**

Horizontal range (r) of the projectile is the distance covered by it from its initial position to the position where is passes y = 0.

Horizontal Range = Horizontal component of velocity (u_{x}) x Total Time of Flight (t)

It is the distance traveled during the flight t_{f}

r = ucosθ x (2usinθ)/g

i.e.

r = (u^{2}sin(2θ))/g

**The Equation of Trajectory (Why Projectile Motion is Parabolic)**

Equations of motion tell us that:

a = t(ucosθ) __K__

b = usinθ x t – ½ x t^{2}/g __L__

where (a,b) is the position of a body at time (t)

By taking Equation **K**and

__L__b = (atanθ – ga^{2})/2u^{2}cos^{2}θ (Equation of Trajectory in Projectile Motion)

Projectile motion is a two-dimensional motion. It can also be said that it is a form of motion in a plane.

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