Preview
IB DP Physics — Unit A: Space, Time and Motion | SL & HL | A.1 Kinematics
📋 What You Will Learn
- Observe and describe projectile motion using real-world examples such as a kicked football or a thrown ball
- Define displacement, velocity, and acceleration components in two dimensions and establish the notation used throughout this topic
- Analyse the independence of horizontal and vertical motion as the fundamental principle of projectile motion
- Apply kinematic equations separately to horizontal and vertical components to solve two-dimensional motion problems
- Derive and interpret the parabolic trajectory equation and the range formula from first principles
- Analyse displacement–time, velocity–time, and trajectory graphs for projectile motion and evaluate common misconceptions
🌍 Real-World Context Watch a goalkeeper kick a football across the pitch. The ball rises, curves gracefully through the air, and lands some distance away — tracing a smooth, arching path. Now watch a stunt motorcyclist launch off a ramp: the bike soars forward and downward simultaneously, landing precisely where the rider calculated. In both cases, the object is moving in two directions at once — horizontally and vertically — and yet the motion can be understood completely using the kinematics you already know. The question is: how do we handle motion in two dimensions at the same time?
🔍 Guiding Question How can the principles of one-dimensional kinematics be extended to analyse the curved path of an object moving under gravity in two dimensions, and what determines how far and how high a projectile travels?
Physical Setup and Diagram
Consider a ball launched from the ground at an angle above the horizontal. Once it leaves the launcher, the only force acting on it is gravity — directed vertically downward. There is no horizontal force (assuming air resistance is negligible). The ball therefore accelerates downward at \( g \approx 9.81 \text{ m s}^{-2} \) while simultaneously moving forward at a constant horizontal speed. The result is the characteristic curved, parabolic path we observe.
Notice several key features in the diagram. The horizontal component of velocity remains the same at every point along the path — there is no horizontal force to change it. The vertical component, however, changes continuously: it decreases as the projectile rises, reaches zero at the apex, and then increases in the downward direction as the projectile falls. The shape of the path is a parabola, and understanding why requires separating the motion into its two independent components.
Core Concepts and Definitions
The key insight of projectile motion is that the horizontal and vertical components of motion are completely independent of each other. Gravity acts only vertically — it cannot affect horizontal motion. This means we can treat the two directions separately, applying the kinematic equations we already know to each direction independently, and then combine the results to describe the full two-dimensional motion.
📖 Key Definition — Projectile A projectile is any object that is given an initial velocity and then moves freely under the influence of gravity alone, with no other forces acting (air resistance is assumed negligible in the IB model).
The motion of a projectile is two-dimensional: it has both horizontal and vertical components of displacement and velocity at every instant. We analyse these components separately using the standard kinematic equations, because the horizontal acceleration is zero and the vertical acceleration is constant at \( -g \) (taking upward as positive).
📖 Key Definition — Principle