This page delves into the mathematical relationships between initial velocity, trigonometric functions, and position vectors in projectile motion.

Definition: Initial velocity (V₀) components are determined using trigonometric relationships: V₀x = V₀cosα and V₀y = V₀sinα.

Highlight: The position vector equations are derived through integration of velocity components.

Example: At initial time t=0, the projectile is located at coordinates (0,h), which helps determine integration constants.

Vocabulary: Position vector (OG) - A vector that describes the location of an object relative to the origin.

This page explains the derivation and characteristics of the projectile's trajectory equation.

Definition: The trajectory equation expresses y as a function of x, resulting in a second-degree polynomial.

Highlight: The trajectory forms a parabola, which is characteristic of projectile motion.

Example: The trajectory equation is derived by eliminating time between the x and y position equations.

Quote: "L'équation de la trajectoire correspond à un polynôme du 2° degrés."

This page covers the energetic aspects of projectile motion, focusing on mechanical energy conservation and work-energy principles.

Definition: Mechanical energy (Em) is the sum of kinetic energy (Ec) and potential energy (Ep).

Highlight: In the absence of friction, mechanical energy is conserved $ΔEm = 0$.

Example: Work done by forces is calculated using W = F × d × cos(α).

Vocabulary: Work-Energy Theorem - States that the change in kinetic energy equals the work done by all forces.

This page introduces the fundamental concepts of projectile motion in a uniform gravitational field. The content focuses on Newton's laws and their application to determine acceleration vectors.

Definition: A uniform gravitational field is represented by g and can be considered constant near Earth's surface.

Highlight: The projectile is only subject to its weight (gravity) as friction is considered negligible.

Example: Using Newton's First Law, the acceleration components are derived as ax = 0 and ay = -g.

Vocabulary: Vector acceleration $a$ - The rate of change of velocity with respect to time.