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 Which Influences the Projectile Motion

  • Horizontal Motion
  • Vertical Motion

Note- Both are independent of each other.

Basic 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

Two Angles of Projection for Same Range

R = v² sin2θ/g ———–     (1)

R = v² sin(180 – 2θ)/g——(2)

Equate (1) & (2), and Solve

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