All the parameters of a horizontal launch can be calculated with the motion equations, assuming a downward acceleration of gravity of 9.8 m/s2. Use the XLC animator to animate the projectile.
Equations of motion
Simple projectile motion refers to the motion of an object in two dimensions (horizontal and vertical) under the influence of gravity while neglecting air resistance. Typically, it involves an object being launched at a certain angle with an initial velocity, and the motion can be described using classical mechanics principles.
The motion of the projectile can be analyzed by splitting it into two independent components: horizontal motion and vertical motion. The horizontal motion is constant velocity motion, while the vertical motion is constant acceleration motion due to gravity.
- Horizontal motion:
- Velocity (Vx): The horizontal velocity remains constant throughout the projectile's flight because no horizontal force acts on the object (ignoring air resistance). Vx = V0 * cos(θ), where V0 is the initial velocity, and θ is the launch angle.
- Displacement (x): The horizontal displacement is calculated as x = Vx * t, where t is the time elapsed.
- Vertical motion:
- Velocity (Vy): The vertical velocity changes due to gravity. Vy = V0 * sin(θ) - g * t, where g is the acceleration due to gravity (approximately 9.81 m/s²).
- Displacement (y): The vertical displacement is calculated as y = V0 * sin(θ) * t - 0.5 * g * t^2.
Some important parameters in projectile motion include:
- Time of flight (T): The total time the projectile stays in the air. T = (2 * V0 * sin(θ)) / g
- Maximum height (H): The highest point the projectile reaches above the launch height. H = (V0^2 * sin^2(θ)) / (2 * g)
- Range (R): The horizontal distance the projectile travels before hitting the ground. R = (V0^2 * sin(2 * θ)) / g
These equations and parameters allow you to analyze and predict the motion of a projectile launched at a certain angle with a given initial velocity, assuming no air resistance and a flat ground.
Full download access to any calculation is available to users with a paid or awarded subscription (XLC Pro).
Subscriptions are free to contributors to the site, alternatively they can be purchased.
Click here for information on subscriptions.