Hang Time
Total time a projectile spends in the air on level ground.
Formula
Variables
Example
8 m/s at 90°: t = 16÷9.81 ≈ 1.63 s
How it works
This formula gives the total time a projectile stays in the air when it lands at the same height it was launched from, such as a ball thrown from level ground. It works because the vertical part of the launch velocity is v\sin\theta; gravity slows that upward motion to zero, then pulls the object back down, so the total flight time is twice the time to rise. The horizontal speed does not affect hang time directly, only the launch angle and the vertical component do.
When to use it
Use this when modelling the airtime of a thrown ball, kicked ball, or launched object that starts and ends at the same height on level ground. It is useful in sports analysis, simple projectile-motion problems, and quick estimates of flight duration.
Worked example, step by step
Suppose a football is kicked at 20 m/s at an angle of 30°. Step 1: Find the vertical launch speed: 20 sin 30° = 20 × 0.5 = 10 m/s Step 2: Substitute into the formula: t = (2 × 10) / 9.81 Step 3: Calculate: t = 20 / 9.81 ≈ 2.04 s Final answer: the football stays in the air for about 2.04 seconds.
Common mistakes to avoid
- Using the launch angle in degrees without calculating sin(θ)
- Forgetting that g is about 9.81 m/s², not 9.8 or 10 unless approximation is acceptable
- Applying the formula when the object lands at a different height than it was launched from
Did You Know?
Michael Jordan's famous hang time was about 0.9 s — physics caps human jumps well under a second.
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