Free Fall Formula
The Formula
v = v_0 + gt \quad ; \quad d = \frac{1}{2}gt^2
When to use: A dropped ball accelerates at the same rate regardless of its mass.
Quick Example
On Earth, objects fall with a = g \approx 9.8 \text{ m/s}^2 (or 10 \text{ m/s}^2 approximation).
What This Formula Means
Motion under the influence of gravity alone, with no air resistance acting on the object.
A dropped ball accelerates at the same rate regardless of its mass.
Worked Examples
Example 1
easyA stone is dropped from a cliff. How far does it fall in 3 \text{ s}? Use g = 9.8 \text{ m/s}^2.
Solution
- 1 Initial velocity: v_0 = 0 (dropped from rest).
- 2 Use the free-fall displacement equation: d = v_0 t + \frac{1}{2}gt^2.
- 3 d = 0 + \frac{1}{2}(9.8)(9) = 44.1 \text{ m}
Answer
d = 44.1 \text{ m}
In free fall, the only force acting is gravity. All objects fall at the same rate regardless of mass (ignoring air resistance), accelerating at g = 9.8 \text{ m/s}^2.
Example 2
mediumA ball is thrown upward with an initial velocity of 20 \text{ m/s}. How high does it go, and how long until it returns? Use g = 9.8 \text{ m/s}^2.
Why This Formula Matters
Fundamental to understanding projectile motion, orbits, and gravitational acceleration.
Frequently Asked Questions
What is the Free Fall formula?
Motion under the influence of gravity alone, with no air resistance acting on the object.
How do you use the Free Fall formula?
A dropped ball accelerates at the same rate regardless of its mass.
Why is the Free Fall formula important in Physics?
Fundamental to understanding projectile motion, orbits, and gravitational acceleration.
What do students get wrong about Free Fall?
Heavier objects fall at the same rate as lighter ones (ignoring air).
What should I learn before the Free Fall formula?
Before studying the Free Fall formula, you should understand: acceleration.