Q: What does Video Analysis of Projectile Motion: Beyond Theory for A-Level Physics cover? A: Master projectile motion using free video analysis software.
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
✓ 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:
Spring launcher: Most repeatable
Ramp release: Good for rolling balls
Hand throw: Mark release point
Catapult/trebuchet: Fun but variable
Pro tip: Record 3-5 launches, analyze best one
Tracker Analysis Step-by-Step
1. Import and Calibrate
Open Tracker → Import video
Set scale: Click meter stick ends
Enter actual length
Set origin at launch point
Define coordinate axes
2. Track the Object
Automatic tracking:
Click "Create" → "Point Mass"
Shift-click on ball in first frame
Tracker follows automatically
Check/correct any errors
Manual tracking (if auto fails):
Click ball center each frame
Use zoom for precision
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:v0=vx02+vy02
Launch angle:θ=tan−1(vx0vy0)
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=v0cosθ⋅ty=v0sinθ⋅t−21gt2
Trajectory equation:y=xtanθ−2v02cos2θgx2
Real-World Deviations
Plot residuals: (measured - theoretical) position
You'll observe:
Shorter range than predicted
Lower maximum height
Asymmetric trajectory (steeper descent)
Decreasing horizontal velocity
Quantifying Air Resistance
For spherical projectiles:
Fdrag=21CDρAv2
Extract drag coefficient:
Measure horizontal deceleration
Calculate drag force
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=gv02sin(2θ)
Maximum range at θ = 45°
Experimental Procedure
Fix launch speed (use spring launcher)
Vary angle: 15°, 30°, 45°, 60°, 75°
Measure range for each
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:
Find frame where vᵧ = 0
Read maximum height directly
Compare with hmax=2gvy02
Calculate % difference
3. Time of Flight
Measured: Count frames from launch to landing
Theoretical:t=g2v0sinθ
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
Position tracking: ±2 pixels typically
Scale calibration: ±1% of reference length
Frame rate accuracy: ±0.1% for phone cameras
Parallax error: If not perfectly perpendicular
Propagating Uncertainties
For initial velocity:
v0δv0=21(vxδvx)2+(vyδvy)2
For range predictions:
δR=R⋅(v02δv0)2+(gδg)2+(δθcotθ)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.
Video Analysis of Projectile Motion: Beyond Theory for A-Level Physics
