Projectile Motion Calculator

Understanding Projectile Motion

Projectile motion follows a parabolic trajectory under the influence of gravity. Here are the key equations and their meanings:

Key Equations

• Time of Flight (T):
  This represents the total time the projectile remains in the air:

  T = (v₀ · sin(θ) + √((v₀ · sin(θ))² + 2 · g · h₀)) / g

  - v₀: Initial velocity
  - θ: Angle of projection
  - h₀: Initial height
  - g: Acceleration due to gravity (default: 9.81 m/s²)
• Maximum Height (H):
  This is the highest vertical point the projectile reaches:

  H = h₀ + (v₀² · sin²(θ)) / (2 · g)

• Range (R):
  This is the total horizontal distance the projectile travels:

  R = v₀ · cos(θ) · T

• Position at Time (t):
  The projectile's position at any given time t is given by:

  Horizontal Position: x = v₀ · cos(θ) · t

  Vertical Position: y = h₀ + v₀ · sin(θ) · t - 0.5 · g · t²

Applications of Projectile Motion

• Sports: Calculating the trajectory of a ball in games like basketball or cricket.
• Military: Designing the trajectory of missiles or projectiles for accuracy.
• Physics Education: Demonstrating concepts of gravity and motion in classrooms.
• Astronomy: Predicting the path of celestial objects like meteors.

Understanding these equations helps in analyzing and predicting the behavior of objects under the influence of gravity. Our calculator simplifies these calculations and provides step-by-step solutions.