Vertical Velocity Component
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Learning zone
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 v_y = 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 v_y 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
- = Launch speed
- = Launch angle
- 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