# Introduction to Projectile Motion

This topic is part of the HSC Physics syllabus under the section Projectile Motion.

### HSC Physics Syllabus

• Analyse the motion of projectiles by resolving the motion into horizontal and vertical components, making the following assumptions:

– a constant vertical acceleration due to gravity
– zero air resistance

### Projectile Motion: Essential Equations

This video introduces the important equations (commonly known as 'suvac' equations) that you will be using to analyse projectile motions of masses.

### Galileo’s Analysis of Projectile Motion

• Projectile motion can be analysed as a form of two-dimensional motion, consisting of a horizontal rectilinear motion (forward-backward or left-right) and a vertical rectilinear motion (up-down).
• The path of projectile motion was first described by Galileo as parabolic and can be resolved into horizontal and vertical components:
• Horizontal component in the absence of zero resistance experience no acceleration
• Vertical component is affected by a constant acceleration due to gravity: 9.8 ms-2. This acceleration (which is a vector quantity) always acts downwards, towards the centre of Earth.
• These ‘components’ are horizontal and vertical velocities of an object in projectile motion. They are independent to one another, meaning changing one component does not affect the other.
• Horizontal velocity is always constant (no acceleration)
• Vertical velocity is not constant (affected by gravity)

Diagram illustrates changes in horizontal (red) and vertical (green) velocities of an object in projectile motion. The maximum height and range (horizontal displacement) are also displayed.

In any projectile motion of mass under the influence of gravity:

• Acceleration due to gravity is directed downward, and is assumed to be constant in magnitude near the surface of Earth (g_{\text{average}} = -9.8)
• Vertical component of velocity decreases in magnitude (vector shortens) when the mass is moving upwards, against gravity.
• Vertical component of velocity is zero at the peak (maximum height) of the parabolic trajectory.
• Vertical component of velocity changes direction and increases in magnitude (vector lengthens) when the mass is moving downwards, in the same direction as acceleration due to gravity.
• The direction and magnitude of horizontal component of velocity remains constant (assuming absence of air resistance)

### Assumptions in Projectile Motion for HSC Physics

There are a few critical assumptions made in Galileo’s analysis of projectile motion and in HSC Physics:

• Air resistance will always be a factor during an object’s motion unless it occurs within a vacuum. Therefore, the horizontal velocity is usually not constant in real life.
• Gravitational acceleration (g) changes with altitude and the projectile’s location on Earth. (9.8 ms-2 is only an average value on the surface of Earth).