When an object falls under the influence of gravity alone, its motion is uniformly accelerated motion. This is free fall.
Basic Knowledge
Free fall (free fall) is motion in which an object falls vertically downward from rest, ignoring air resistance and under the influence of gravity alone. The initial velocity is v₀ = 0, and the acceleration is gravitational acceleration g ≈ 9.8 m/s²(vertically downward).
Substitute v₀ = 0 and a = g into the three equations of uniformly accelerated motion:
① v = gt
② y = ½gt²
③ v² = 2gy
(y is the falling distance, and downward is positive)
Vertically downward projection is uniformly accelerated motion with an initial velocity v₀ > 0: v = v₀ + gt, y = v₀t + ½gt²
Vertically upward projection uses upward as positive and a = -g: v = v₀ - gt, y = v₀t - ½gt², and v = 0 at the highest point.
Gravitational acceleration g = 9.8 m/s²(Sometimes approximated as g = 10 m/s² depending on the problem).
Free fall (free fall)（Motion in which an object falls from an initial velocity of 0 under the influence of gravity alone）
Gravitational acceleration g（≈ 9.8 m/s². It varies slightly with latitude and altitude at Earth's surface）
Vertically downward projection（Uniformly accelerated motion in which an object is thrown vertically downward with an initial velocity > 0）
Vertically upward projection（An initial velocity is given upward. v = 0 at the highest point）
Ignoring air resistance（Usually ignored in calculations at the level of basic physics）
y = ½gt²（Equation for the falling distance in free fall）
Further Study (Background and Significance)
From experiments with balls rolling down an inclined plane, Galileo discovered that the falling distance is proportional to the square of time. He overturned the common belief that “heavier objects fall faster” and showed that objects fall with the same acceleration regardless of mass(the famous experiment in which a feather and a metal ball fall simultaneously in a vacuum).
On Earth, gravitational acceleration g is approximately 9.78 m/s² near the equator and approximately 9.83 m/s² near the poles, so it differs slightly. This is because Earth is not a perfect sphere and because of the effect of centrifugal force caused by its rotation.
In vertically upward projection, the time from the highest point back to the same height is symmetrical for the ascent and descent. Also, the speed when the object returns to the ground equals its initial speed(also confirmed by the law of conservation of energy).
- Free fall: v₀=0, a=g=9.8 m/s²
- v = gt, y = ½gt², v² = 2gy
- g is the same regardless of mass(in a vacuum)
- Highest point of upward projection: v = 0
- Upward projection: a = -g(when upward is positive)
- Speed when returning to the ground = magnitude of the initial velocity
- g ≈ 9.8 m/s²(It may also be approximated as ≈10 m/s²)
Points to Note (Common Confusions)
① Free fall has an initial velocity of 0. A downward throw has an initial velocity. Do not confuse them. ② The acceleration of vertically upward projection is downward. When upward is positive, a = -g. It is incorrect to say “the acceleration is 0 at the highest point.” ③ In free fall, objects fall with the same acceleration regardless of whether they are heavy or light(when air resistance is ignored). ④ The time for an object to fall from height h is found from h = ½gt² as t = √(2h/g).
Practice
- An object was released from rest from a building 20 m high. Find the time until it reaches the ground and its velocity at that moment(g = 10 m/s²).
- An object was thrown vertically upward with an initial velocity of 15 m/s. Find the height of the highest point(g = 10 m/s²).
- Explain the relationship between falling distance and time in free fall.