Vertical Velocity Component
Worked example: 20 m/s at 30° → 10 m/s — press Try an example to run it live, then adjust anything.
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Vertical Velocity Component explained
The vertical slice of the launch velocity, v sin θ, is the only part gravity ever touches — it decides how high the projectile climbs and how long it hangs in the air. A ball thrown at 20 m/s and 30° leaves with = 20 × sin 30° = 10 m/s, rises for about a second, then comes back down through the launch height at 10 m/s downward, the flight being perfectly symmetric in a vacuum.
Long-jumpers live inside this trade-off: too shallow an angle and is too small to stay airborne, too steep and the horizontal component collapses. Real jumpers take off near 20°, not the textbook 45°, because a human leg cannot generate the same launch speed in a steep, heavily loaded push-off — a reminder that the mathematically optimal angle is optimal only when v is genuinely independent of θ.
Vertical Velocity Component formula
- = Vertical velocity (m/s)
- = Launch speed (m/s)
- = Launch angle (°)
Missing one of these? Work it out first, then come back
- Vertical velocity — Linear Momentum (p = mv), Power from Force and Velocity (P = Fv)
- Launch speed — Projectile Range on Level Ground, Projectile Maximum Height
- Launch angle — Projectile Range on Level Ground, Projectile Maximum Height