Projectile motion

35 topics across 5 chapters

Chapter 1

Prerequisites (math + 1D kinematics)

Coordinate systems, axes choice, and sign conventions (practice setup on diagrams)

Trigonometry essentials (sin/cos/tan, special angles, inverse trig)

Constant-acceleration kinematics in 1D (derive and apply the 4 main equations)

Vector decomposition for velocity and acceleration

2 subtopics

Drill: resolve a launch velocity into components for multiple angles (including quadrants)

Drill: convert between (vx, vy) and (speed, angle) using trig + inverse trig

Chapter 2

Core ideal-projectile model (no air resistance)

↗ Vector decomposition for velocity and acceleration (see Chapter 1)

Independence of horizontal and vertical motion (ax=0, ay=-g)

Derive parametric equations x(t), y(t) from kinematics

Eliminate time to get the trajectory equation y(x) (parabola form)

Key results on level ground: time to peak, max height, time of flight, range

2 subtopics

Compute time to peak and maximum height from vy(t) and y(t) (worked examples)

Compute time of flight and range on level ground (worked examples + edge cases)

Chapter 3

Standard problem-solving patterns

Forward problems: given v0 and angle, find position/velocity at a time and the landing point

Inverse problems: given range/height/time, solve for launch speed and/or angle

Method choices: which equation to use, units checks, and reasonableness checks

Different launch and landing heights (solve with y(t) + root selection)

Chapter 4

Variations and advanced extensions

↗ Different launch and landing heights (solve with y(t) + root selection) (see Chapter 3)

Moving launch platform / relative velocity (Galilean transformation)

Air resistance: qualitative effects and why the parabola model breaks

Air resistance: numerical solution approach (set up ODEs for drag)

1 subtopics

Implement a simple integrator (Euler or RK4) to simulate drag and compare to no-drag

Projectile motion on an incline (coordinate choice and impact condition)

Chapter 5

Lab, simulation, and physical intuition

Experiment: measure a projectile path with phone video (video analysis workflow)

2 subtopics

Video analysis step: calibrate scale, choose axes, and extract (x,y,t) data points

Video analysis step: fit y(x) to a parabola and estimate g (discuss uncertainty)

Build a simulation to connect formulas to motion (ideal + comparison)

2 subtopics

Simulation task: generate x(t), y(t) and plot the trajectory for chosen v0 and angle

Simulation task: verify formulas (range, max height) against the simulated motion

Common misconceptions (e.g., “speed is constant”, “peak happens at half time”) and fixes

Uncertainty and error basics (measurement error, fitting error, reporting results)