Free Fall and Projectile Motion

Free Fall

In free fall, a body moves under the action of gravity alone: g ≈ 9,8 ≈ 10 m/s².

• Velocity: v = g·t.
• Height: h = g·t²/2.
• Velocity and height: v² = 2gh.

Vertical Projection

• Velocity of a body thrown upward: v = v₀ − gt.
• Maximum height: H = v₀²/(2g).
• Time of ascent: t = v₀/g.
• At the highest point the velocity is zero, but the acceleration is equal to g.

Horizontal and Angled Projection

Projection	Formulas
Horizontal	x = v₀·t; y = g·t²/2
At an angle	range L = v₀²·sin2α/g

• At 45° it travels the farthest, because sin90° = 1.
• At 30° and 60° the range is the same, but the height is different.
• These formulas are valid when air resistance is neglected and the body lands back at the level from which it was thrown.

Examples

• The time of fall from 125 m is t = √(2·125/10) = 5 s.
• A body thrown upward with v₀ = 40 m/s rises to H = 1600/20 = 80 m.