EQUATION

Projectile Time of Flight

Gives the total airborne time for a projectile launched from and landing on the same horizontal level

§ 01

The equation

EQ.PROJECTILE-TIME-OF-FLIGHT

T = \frac{2v_0\sin\theta}{g}

§ 02

What it solves

Gives the total airborne time for a projectile launched from and landing on the same horizontal level. Knowing T unlocks the horizontal range and the timing of any in-flight event.

§ 03

When to use it

Symmetric projectile trajectories — same launch and landing height, constant g, negligible air resistance.

§ 04

When NOT to use it

Invalid when launch and landing heights differ; use the full position-time relation with y = 0 instead. Fails when air resistance is significant or when g varies (very high altitude).

§ 05

Common mistakes

Forgetting the factor of 2 — T = 2·v_0·sin θ / g, not v_0·sin θ / g (which is only the time to peak). Using g = 9.8 m/s² when the problem specifies a different value. Confusing θ with the complementary angle.

§ 06

Topics that use this equation

vectors and projectile motion