Projectile Motion & Trajectory for a Football
Analyzing the 2D parabolic flight path of a standard Football (mass 0.43 kg).A spiral touchdown pass or field goal kick.
Trajectory curves and apex altitudes are modeled in real-time on the HTML5 canvas below using classical two-dimensional kinematic equations (R = v²·sin(2θ)/g).
Projectile Motion & Parabolic Trajectory
Classical 2D Kinematics in Vacuum (Halliday & Resnick)
Total horizontal distance traveled until impact.
Peak vertical altitude at trajectory apex.
Total airborne duration from launch to ground.
Football Flight Metrics Across Launch Angles (v₀ = 25 m/s)
| Launch Angle (θ) | Range (R) | Max Apex Height (H_max) | Flight Duration (T) | Trajectory Type |
|---|---|---|---|---|
15° | 31.87 m | 2.13 m | 1.32 s | Flat Drive / Low Line |
30° | 55.19 m | 7.97 m | 2.55 s | Optimal Balistic Arc |
45°Max Range | 63.73 m | 15.93 m | 3.61 s | Optimal Balistic Arc |
60° | 55.19 m | 23.90 m | 4.42 s | Optimal Balistic Arc |
75° | 31.87 m | 29.73 m | 4.92 s | High Lob / Pop-up |
Explore Other Kinematics & Motion Calculators
Frequently Asked Questions
Q1.What launch angle provides maximum range for a Football?
In a vacuum (or neglecting air resistance), maximum horizontal range for any projectile is achieved at an exact launch angle of 45°, where sin(2θ) = 1. At 25 m/s, the theoretical maximum range is 63.7 meters.
Q2.Does the 0.43kg mass of the Football alter its parabolic trajectory?
In idealized classical kinematics without atmospheric drag, trajectory is strictly governed by initial velocity v₀, launch angle θ, and gravitational acceleration g—completely independent of mass. In real air, drag and Magnus spin force introduce minor deviations.
Q3.How long is a Football in the air at 25 m/s and 35°?
Airborne hang time is calculated using T = 2v₀ · sin(θ) / g. For 25 m/s at 35°, flight duration is 2.92 seconds.
skymotion20-20).Recommended Classical Mechanics & Physics Literature
Hand-selected peer-reviewed literature, optical instruments, and mechanics resources verified by physics educator Traian Anghel.
The Feynman Lectures on Physics, Vol. 1
By Richard Feynman, Robert Leighton & Matthew Sands. Mechanics, radiation, kinetics, and heat.
Classical Mechanics by John R. Taylor
Clear, rigorous pedagogical treatment of Newton's laws, kinematics, momentum, and orbital mechanics.
Physics for Scientists and Engineers
By Raymond A. Serway & John W. Jewett. Comprehensive kinetic energy, work, and friction mechanics.