**Projectile Motion**

**Definition**

Projectile Motion is a type of motion in which a particle or an object under the influence of gravity only, when is in flight through the atmosphere. It is not being propelled by any other source or any fuel. It is studied under the 2-dimensional type of motion.

- The path followed is called trajectory.

**Types of Projectile Motion**

**Horizontal Projectile-**If projected horizontally with a certain velocity at a certain height.**Oblique Projectile-**If projected with a certain angle with horizontal.

**Motions that Influences the Projectile Motion**

- Horizontal Motion
- Vertical Motion

*Note- Both are independent of each other.*

**Read Also- Differentiation Notes**

**Formula Used:**

- θ is with Horizontal
- t = Time
- x = Distance
- g = Gravity
- v = Velocity
- h= Maximum Vertical Height

**Horizontal Projectile**

**Time of Flight**

T= (√(2h/g))

**Horizontal Range (R)**

R = v× (√(2h/g))

in other words Distance = velocity×time

**Oblique Projectile**

**Horizontal Motion Path**

t = x/v cosθ

**Vertical Motion Path**

y = x tanθ – (gx²/2v² cos²θ)

**Maximum Height**

H = v² sin²θ/2g

if the angle (θ) is with *vertical;* change *sin* θ* to cos* θ

**Horizontal Range (R)**

R = v² sin2θ/g

if the angle (θ) is with vertical then there will be *no change*

**Maximum Horizontal Range**

R = v²/g

at sin2θ = 1 or θ = 45 degree

**Time of Flight (T)**

T = 2v sinθ/g

if the angle (θ) is with vertical; **change** *sin* θ* to cos* θ

Read More: Convection Heat Transfer Process

**Two Angles of Projection for Same Range**

R = v² sin2θ/g ———– (1)

R = v² sin(180 – 2θ)/g——(2)

Equate (1) & (2), and Solve

**Read More: Indefinite Integration Formulas**

**Read More: Polynomials: Definitions, Types, Factorization**

It’s is very useful