Projectile motion is the motion of an object projected into the air, subject only to the force of gravity. Here are the key equations:
Horizontal Motion:
* Horizontal Velocity (Vx): Vx = V₀ * cos(θ)
* V₀ = Initial Velocity
* θ = Launch Angle
* Horizontal Displacement (x): x = V₀t * cos(θ)
* t = Time
Vertical Motion:
* Vertical Velocity (Vy): Vy = V₀ * sin(θ) - gt
* g = Acceleration due to gravity (approximately 9.8 m/s²)
* Vertical Displacement (y): y = V₀t * sin(θ) - (1/2)gt²
* Final Vertical Velocity (Vyf): Vyf = V₀ * sin(θ) - gt
Other Useful Equations:
* Time of Flight (t): t = 2V₀ * sin(θ) / g
* Range (R): R = V₀² * sin(2θ) / g
* Maximum Height (H): H = V₀² * sin²(θ) / (2g)
Assumptions:
* Air resistance is negligible.
* Gravity is constant and acts downward.
* The object is launched from a point that is considered the origin (x = 0, y = 0).
Notes:
* These equations are derived from the basic kinematic equations of motion.
* The horizontal and vertical motions are independent of each other.
* You can use these equations to solve for various parameters of projectile motion, such as the initial velocity, launch angle, time of flight, range, and maximum height.
Example:
Let's say you throw a ball with an initial velocity of 20 m/s at an angle of 30 degrees above the horizontal.
* Horizontal Velocity: Vx = 20 * cos(30°) = 17.32 m/s
* Vertical Velocity: Vy = 20 * sin(30°) = 10 m/s
* Range: R = (20² * sin(2 * 30°)) / 9.8 = 35.34 m
* Maximum Height: H = (20² * sin²(30°)) / (2 * 9.8) = 5.1 m
These equations allow you to analyze and predict the trajectory of projectiles in a wide range of applications.
