Video Analysis of Projectile Motion: Beyond Theory for A-Level Physics

TL;DR
Your phone camera + free Tracker software = professional motion lab. Capture projectiles at 240fps, extract position data every 0.004s, and see exactly how air resistance ruins those perfect parabolas. This guide shows how to measure initial velocity to ±1%, prove range equations, and handle every projectile variation in H2 Physics.

Why Video Analysis Beats Traditional Methods

Traditional projectile experiments rely on:

• Crude measurements (where did it land?)
• Idealized conditions (ignoring air resistance)
• Single data points (initial and final positions)

Video analysis provides:

• Complete trajectory: 100+ position measurements
• Real-world physics: Air resistance effects visible
• Multiple parameters: Extract v₀, θ, drag coefficient
• Uncertainty analysis: Statistical fitting to curves

Equipment and Software Setup

Hardware Requirements

Camera Options (in order of preference):

1. Smartphone at 240fps (iPhone 6+, most Android flagships)
2. Action camera (GoPro at 120fps+)
3. Standard phone at 60fps (acceptable for slower projectiles)
4. DSLR with high-speed mode (overkill but excellent)

Other Equipment:

• Tripod (essential for stable footage)
• Meter stick or known-length object (for scale)
• Bright, uniform background
• Good lighting (outdoor or strong lamps)

Software: Tracker (Free and Powerful)

Download from: physlets.org/tracker/

Key features:

• Frame-by-frame position tracking
• Automatic object detection
• Built-in physics models
• Direct export to spreadsheet
• Works on Windows/Mac/Linux

Setting Up Your Experiment

Camera Positioning

1. Perpendicular view: Camera exactly 90° to motion plane
2. Far enough back: Entire trajectory in frame
3. Level camera: Use spirit level app
4. Fixed focus: Disable autofocus
5. Maximum frame rate: 120fps minimum preferred

Calibration Requirements

In every video, include:

• Meter stick or ruler in motion plane
• Vertical and horizontal references
• Clear launch point marker
• Landing zone markers

Projectile Options

Beginner: Tennis ball, foam ball Intermediate: Ping pong ball (air resistance effects) Advanced: Water balloons (shape changes!) Precise: Steel ball bearings

Recording Your Video

Pre-Launch Checklist

✓ Camera recording at high frame rate
✓ Entire expected path in frame
✓ Scale object clearly visible
✓ Good contrast (object vs background)
✓ No camera shake (use timer/remote)

Launch Techniques

For consistent launches:

1. Spring launcher: Most repeatable
2. Ramp release: Good for rolling balls
3. Hand throw: Mark release point
4. Catapult/trebuchet: Fun but variable

Pro tip: Record 3-5 launches, analyze best one

Tracker Analysis Step-by-Step

1. Import and Calibrate

1. Open Tracker → Import video
2. Set scale: Click meter stick ends
3. Enter actual length
4. Set origin at launch point
5. Define coordinate axes

2. Track the Object

Automatic tracking:

1. Click "Create" → "Point Mass"
2. Shift-click on ball in first frame
3. Tracker follows automatically
4. Check/correct any errors

Manual tracking (if auto fails):

1. Click ball center each frame
2. Use zoom for precision
3. Keyboard shortcuts speed process

3. View the Data

Tracker instantly generates:

• x(t) and y(t) graphs
• vₓ(t) and vᵧ(t) graphs
• Trajectory y(x) plot
• Data table with all values

Extracting Physics Parameters

Initial Velocity Components

From Tracker's velocity graphs:

• vₓ₀: Initial horizontal velocity (should be constant)
• vᵧ₀: Initial vertical velocity

Initial speed: \(v_0 = \sqrt{v_{x0}^2 + v_{y0}^2}\)

Launch angle: \(\theta = \tan^{-1}\left(\frac{v_{y0}}{v_{x0}}\right)\)

Acceleration Measurement

Without air resistance:

• aₓ = 0
• aᵧ = -g ≈ -9.81 m/s²

With air resistance:

• aₓ < 0 (horizontal deceleration)
• |aᵧ| < g (reduced downward acceleration)

Fit straight line to vᵧ(t) → gradient = -g

Comparing Theory vs Reality

Ideal Projectile Motion

Position equations: \[x = v_0\cos\theta \cdot t\] \[y = v_0\sin\theta \cdot t - \frac{1}{2}gt^2\]

Trajectory equation: \[y = x\tan\theta - \frac{gx^2}{2v_0^2\cos^2\theta}\]

Real-World Deviations

Plot residuals: (measured - theoretical) position

You'll observe:

1. Shorter range than predicted
2. Lower maximum height
3. Asymmetric trajectory (steeper descent)
4. Decreasing horizontal velocity

Quantifying Air Resistance

For spherical projectiles: \[F_\text{drag} = \frac{1}{2}C_D\rho Av^2\]

Extract drag coefficient:

1. Measure horizontal deceleration
2. Calculate drag force
3. Solve for C_D

Typical values:

• Smooth sphere: C_D ≈ 0.47
• Tennis ball: C_D ≈ 0.51
• Ping pong ball: C_D ≈ 0.40

Range vs Angle Investigation

Theoretical Optimum

Without air resistance: \[R = \frac{v_0^2\sin(2\theta)}{g}\]

Maximum range at θ = 45°

Experimental Procedure

1. Fix launch speed (use spring launcher)
2. Vary angle: 15°, 30°, 45°, 60°, 75°
3. Measure range for each
4. Plot R vs θ

What You'll Discover

With air resistance:

• Optimal angle < 45° (typically 35-42°)
• Higher angles affected more
• Depends on projectile mass/size

Analysis enhancement:

• Plot R/R_max vs θ
• Compare different balls
• Extract optimal angle

Common Exam Applications

1. "Monkey and Hunter" Problem

Setup: Aim at target, which drops when fired

Video proof:

• Track both projectile and falling target
• Show collision regardless of launch speed
• Verify y_projectile = y_target at impact

2. Maximum Height Analysis

From video data:

1. Find frame where vᵧ = 0
2. Read maximum height directly
3. Compare with \(h_\text{max} = \frac{v_{y0}^2}{2g}\)
4. Calculate % difference

3. Time of Flight

Measured: Count frames from launch to landing Theoretical: \(t = \frac{2v_0\sin\theta}{g}\)

Explain why measured < theoretical

4. Projectile from Height

Launch from table/cliff:

• Asymmetric trajectory
• Time up ≠ time down
• Landing velocity > launch velocity

Uncertainty Analysis

Sources of Uncertainty

1. Position tracking: ±2 pixels typically
2. Scale calibration: ±1% of reference length
3. Frame rate accuracy: ±0.1% for phone cameras
4. Parallax error: If not perfectly perpendicular

Propagating Uncertainties

For initial velocity: \[\frac{\delta v_0}{v_0} = \frac{1}{2}\sqrt{\left(\frac{\delta v_x}{v_x}\right)^2 + \left(\frac{\delta v_y}{v_y}\right)^2}\]

For range predictions: \[\delta R = R \cdot \sqrt{\left(\frac{2\delta v_0}{v_0}\right)^2 + \left(\frac{\delta g}{g}\right)^2 + (\delta\theta\cot\theta)^2}\]

Improving Precision

• Use highest frame rate available
• Maximize pixels per meter (zoom appropriately)
• Multiple trials and averaging
• Careful sub-pixel tracking

Advanced Investigations

1. Magnus Effect (Spinning Ball)

Add spin to projectile:

• Curved trajectory visible
• Compare topspin vs backspin
• Measure lateral deviation
• Link to Bernoulli principle

2. Variable Mass Projectiles

Water balloons or leaking containers:

• Mass changes during flight
• Affects trajectory shape
• Model with differential equations

3. Multi-Stage Analysis

Track sports movements:

• Basketball shot (release → rim)
• Soccer ball (kick → goal)
• Badminton clear (hit → landing)

Extract technique parameters for optimization

Excel/Python Analysis Template

Basic Analysis Structure

Columns:

• A: Time (s)
• B: x position (m)
• C: y position (m)
• D: vₓ = Δx/Δt
• E: vᵧ = Δy/Δt

Key formulas:

• Initial velocity: =SQRT(D2^2 + E2^2)
• Launch angle: =DEGREES(ATAN(E2/D2))
• Theory vs actual: =C_actual - C_theory

Python Enhancement

import numpy as np
from scipy.optimize import curve_fit

# Fit trajectory with drag
def trajectory_drag(x, v0, theta, cd):
    # Include air resistance model
    return y_positions

# Extract parameters
params, covariance = curve_fit(trajectory_drag, x_data, y_data)

Troubleshooting Common Issues

"Tracker loses the ball"

Solutions:

• Increase contrast (edit video brightness)
• Use colored ball against plain background
• Manual tracking for difficult sections
• Try different tracking algorithms

"Trajectory looks stepped/jagged"

Causes:

• Low frame rate
• Poor lighting (motion blur)
• Compression artifacts

Fix: Reshoot with better settings

"Results way off theory"

Check:

• Calibration accuracy
• Coordinate system orientation
• Unit conversions
• Air resistance for light objects

Exam-Ready Skills Checklist

✓ Set up perpendicular view with scale reference
✓ Track object precisely through entire flight
✓ Extract v₀ and θ from initial frames
✓ Compare with theory using proper equations
✓ Quantify air resistance effects
✓ Optimize launch angle experimentally
✓ Calculate uncertainties throughout
✓ Explain all deviations from ideal behavior

Master video analysis and you transform abstract equations into visible physics. You'll predict basketball shots, optimize throwing techniques, and understand why real projectiles never quite match those perfect parabolas - essential insights for both exams and life.