Projectile Time of Flight

Time of flight: t = 2·v₀·sin θ / g

For oblique launch returning to the same level, total flight time is t = 2·v₀·sin θ / g — twice the rise time, since ascent and descent are symmetric in vacuum. When the launch and landing heights differ (h₀ ≠ h_final), the time follows the quadratic h_final = h₀ + v₀·sin θ·t − ½·g·t², solved for t. Example: v₀ = 50 m/s at θ = 30° on flat ground gives t ≈ 5.1 s. Air resistance shortens flight time and makes the trajectory asymmetric — the descent becomes steeper than the ascent, and the impact point shifts inward.

Applications

Sports timing (ball return time on goal kicks, hang time in basketball — a 0.9 m vertical leap stays airborne ~0.86 s), free-fall analysis, ballistics (TOF — Time of Flight is a core artillery parameter), drop tests from tall structures (Burj Khalifa ~828 m gives ~13 s in vacuum), athletics (long jump, high jump biomechanics).

FAQ

Why is ascent time equal to descent time? In vacuum, gravity is the only force; the projectile decelerates upward at g and accelerates downward at g, so symmetric speeds give symmetric times.

How does launch height affect flight time? Launching from above the landing level adds extra descent — the quadratic in t yields a longer total flight time than the simple formula predicts.

Does air resistance change t? Yes — drag slows the projectile, reducing both the peak height reached and the total flight time, and breaks the ascent/descent symmetry.