Parabolic Motion and Projectile Equations
This page provides a comprehensive overview of parabolic motion and the equations governing projectile motion. It covers both the horizontal and vertical components of motion, as well as an example problem to illustrate the concepts.
The page begins by presenting the general equations for projectile motion:
Definition: Parabolic motion equations:
- x = x₀ + v₀ₓt + ½aₓt² horizontalaxis
- y = y₀ + v₀ᵧt + ½aᵧt² verticalaxis
These equations describe the position of a projectile at any given time, considering initial position, initial velocity, and acceleration in both x and y directions.
The page then breaks down the motion into its horizontal and vertical components:
-
Horizontal motion x−axis:
Characterized by uniform motion
No forces act along this axis accordingtoNewton′ssecondlaw
Equation: x = x₀ + v₀ₓt
-
Vertical motion y−axis:
Affected by gravity
Uniformly accelerated motion
Equations:
y = y₀ + v₀ᵧt - ½gt²
vᵧ = v₀ᵧ - gt
Highlight: The horizontal component of motion is uniform constantvelocity, while the vertical component is uniformly accelerated due to gravity.
An example problem is presented to demonstrate the application of these concepts:
Example:
- Initial velocity v0 = 20 m/s
- Launch angle θ = 30°
- Initial height y0 = 10 m
The problem is solved by breaking down the initial velocity into its x and y components:
- v₀ₓ = v₀ cos30° = 17.3 m/s
- v₀ᵧ = v₀ sin30° = 10 m/s
The equations for the projectile's motion are then given:
- x = 17.3t horizontalposition
- y = 10 + 10t - 4.9t² verticalposition
- vᵧ = 10 - 9.81t verticalvelocity
Vocabulary:
- Moto rettilineo uniforme: Uniform rectilinear motion constantvelocity
- Moto rettilineo uniformemente accelerato: Uniformly accelerated rectilinear motion
This comprehensive breakdown of parabolic motion provides students with a solid foundation for solving esercizi sul moto parabolico exercisesonparabolicmotion and understanding the principles behind projectile trajectories.