Time of Flight
Simple Explanation
The time of flight is the total time a projectile spends in the air, from the moment it is launched until it returns to the same height it was launched from.
Why Do We Need It?
Knowing the time of flight is essential for finding how far a projectile travels (its range) and for timing events involving projectiles, like when a thrown object will land.
Formula
Time of Flight (Projectile Motion)
T = 2u sinθ / g
The total time a projectile stays in the air, from launch until it returns to its launch height.
- T
- — Time of flight, in seconds
- u
- — Initial launch speed, in m/s
- θ
- — Launch angle above the horizontal
- g
- — Acceleration due to gravity, 9.8 m/s²
When to use it: Use to find how long a projectile launched at an angle stays airborne before landing at the same height it was launched from.
Worked Example
Finding the time of flight
A ball is launched at 25 m/s at an angle of 40° above the horizontal. Find its time of flight (g = 9.8 m/s², sin40° ≈ 0.643).
Why Does This Work?
The projectile's vertical motion is symmetric: the time to rise to maximum height equals the time to fall back down to the launch height, since gravity's deceleration going up mirrors its acceleration coming down. The formula is derived by finding when the vertical displacement returns to zero.
Real-Life Example
Timing a basketball free throw
A basketball player launches the ball toward the hoop at a specific angle and speed.
The time of flight formula tells a coach (or a physics-minded player) exactly how long the ball is airborne — useful for understanding shot arcs and comparing different launch angles and speeds.
Practice
A projectile is launched at 30 m/s at 90° (straight up). Find its time of flight (g = 9.8 m/s², sin90° = 1).
MediumCommon mistake
Forgetting to use the LAUNCH ANGLE'S sine, not the angle itself, in the formula — and forgetting the factor of 2, which accounts for both the rise and the fall.
Quick Review
- T = 2u sinθ / g gives the total time a projectile is airborne.
- The rise time and fall time are equal (symmetric motion).
- Time of flight depends on launch speed and angle, not on mass.