Vertical Velocity Component

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.