Lesson 12: Gravity


From the time of Aristotle (384-322 BC) until the late 1500’s, gravity was believed to act differently on different objects.


Galileo Galilei was the first major scientist to refute (prove wrong) Aristotle’s theories.

ag = g = 9.81m/s2

ag = g = acceleration due to gravity

Since gravity is just an acceleration like any other, it can be used in any of the formulas that we have used so far.

Examples of Calculations with Gravity

Example 1: A ball is thrown up into the air at an initial velocity of 56.3m/s. Determine its velocity after 4.52s have passed.

In the question the velocity upwards is positive, and I’ll keep it that way. That just means that I have to make sure that I use gravity as a negative number, since gravity always acts down.

vf = vi + at

= 56.3m/s + (-9.81m/s2)(4.52s)

vf = 12.0 m/s

This value is still positive, but smaller. The ball is slowing down as it rises into the air.

Example 2: I throw a ball down off the top of a cliff so that it leaves my hand at 12m/s. Determine how fast is it going 3.47 seconds later.

In this question I gave a downward velocity as positive. I might as well stick with this, but that means I have defined down as positive. That means gravity will be positive as well.

vf = vi + at

= 12m/s + (9.81m/s2)(3.47s)

vf = 46 m/s

Here the number is getting bigger. It’s positive, but in this question I’ve defined down as positive, so it’s speeding up in the positive direction.

Example 3: I throw up a ball at 56.3 m/s again. Determine how fast is it going after 8.0s.

We’re defining up as positive again.

vf = vi + at

= 56.3m/s + (-9.81m/s2)(8.0s)

vf = -22 m/s

Why did I get a negative answer?

The Rules

There’s a few rules that you have to keep track of. Let’s look at the way an object thrown up into the air moves.

As the ball is going up…

As the ball is coming down…

Example 4: I throw my ball up into the (again) at a velocity of 56.3 m/s.

a) Determine how much time does it take to reach its maximum height.

a = (vf - vi) / t

t = (vf - vi) / a

= (0 - 56.3m/s) / -9.81m/s2

t = 5.74s

b) Determine how high it goes.

vf2 = vi2 + 2ad

d = (vf2 = vi2) / 2a

= (0 - 56.32) / 2(-9.81m/s2)

d = 1.62e2 m

c) Determine how fast is it going when it reaches my hand again.


You might have heard people in movies say how many "gee’s" they were feeling.