Table of Contents
What Is Time of Flight?
Time of flight is total airtime of a projectile from launch to landing. It decomposes into horizontal (constant velocity) and vertical (constant acceleration) components. Maximum range occurs at 45 degrees for flat ground; with air resistance the optimal drops to 30-40 degrees.
At 45 degrees, horizontal and vertical velocity components are equal, giving the best balance between distance and airtime. Higher angles give more height but less range; lower angles give flatter trajectories but shorter airtime.
Equations
T = 2v0sin(θ)/g
H = v0²sin²(θ)/(2g)
R = v0²sin(2θ)/g
Range vs Angle (50 m/s)
| Angle | Range | Time | Height |
|---|---|---|---|
| 15° | 127 m | 2.6 s | 8.5 m |
| 30° | 221 m | 5.1 s | 32 m |
| 45° | 255 m | 7.2 s | 64 m |
| 60° | 221 m | 8.8 s | 96 m |
FAQ
Why is 45° optimal?
R = v²sin(2θ)/g is maximized when sin(2θ)=1, at θ=45°. With air resistance, optimal angle drops to about 30-40°.