Projectile Motion & Trajectory for a Tennis Ball
Analyzing the 2D parabolic flight path of a standard Tennis Ball (mass 0.057 kg).A flat first serve or aggressive topspin baseline drive.
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.
Tennis Ball Flight Metrics Across Launch Angles (v₀ = 35 m/s)
| Launch Angle (θ) | Range (R) | Max Apex Height (H_max) | Flight Duration (T) | Trajectory Type |
|---|---|---|---|---|
15° | 62.46 m | 4.18 m | 1.85 s | Flat Drive / Low Line |
30° | 108.18 m | 15.61 m | 3.57 s | Optimal Balistic Arc |
45°Max Range | 124.92 m | 31.23 m | 5.05 s | Optimal Balistic Arc |
60° | 108.18 m | 46.84 m | 6.18 s | Optimal Balistic Arc |
75° | 62.46 m | 58.27 m | 6.89 s | High Lob / Pop-up |
Explore Other Kinematics & Motion Calculators
Frequently Asked Questions
Q1.What launch angle provides maximum range for a Tennis Ball?
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 35 m/s, the theoretical maximum range is 124.9 meters.
Q2.Does the 0.057kg mass of the Tennis Ball 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 Tennis Ball in the air at 35 m/s and 15°?
Airborne hang time is calculated using T = 2v₀ · sin(θ) / g. For 35 m/s at 15°, flight duration is 1.85 seconds.
skymotion20-20).Recommended Classical Mechanics & Physics Literature
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The Feynman Lectures on Physics, Vol. 1
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