# Falling Objects

Gravity: It's not just a good idea, it's the law! Near the surface of the Earth and in the absence of air resistance, objects in free fall will have a uniform acceleration of about 9.8 m/s2. This is the value of acceleration due to gravity, which we commonly refer to as g.

• Frequently we will refer to acceleration in terms of g. 1 g = 9.8 m/s2. For example, if a pilot in a jet is experiencing an acceleration of 24 m/s2, then he is also experiencing an acceleration of (24 m/s2 / 9.8   m/s2=) 3.5 gs.

We are going to make a bold leap here and completely ignore the effects of air resistance (drag) and make the following statement: All objects fall with the same downward acceleration due to gravity - 9.8 m/s2 I'm making a big deal of this because it is an important point when we start talking about projectile motion and independent movement in the x-axis and the y-axis. It is thought that Galileo was the first to figure this out and write about it accurately, although he was unable to test his hypothesis in a vacuum. How do we make use of this?

Consider 2 Cases:

In case 1, we are at the top of a 100 meter building and we drop a ball off. Let's call "down" negative, with the value of g = -9.8 m/s2. Using our displacement and velocity formulas

x = xo + vot + ½ at2 and v = vo+ at

let xo = 0m, vo = 0m/s, and a = g.
Then, x = .5gt2, or
x = - 4.9t2. Now we can generate a table of values for position and velocity:

 Time Displacement Velocity 0 sec 0 meters 0 m/s 1 sec -4.9 m -9.8 m/s 2 sec -19.6 m -19.6 m/s 3 sec -44.1 m -29.4 m/s 4 sec -78.4 m -39.2 m/s 4.5 sec -100 m -44.1m/s

One thing to notice is, while velocity is increasing linearly, the displacement is increasing exponentially as a square of the time elapsed.

In case 2, we will throw a ball up in the air with a constant velocity - say 20 m/s. The acceleration on the ball is always -9.8 m/s2(as long as we ignore air resistance and gravity is the only force acting on the ball). Thus, the ball will rise to a maximum height where the velocity of the ball is 0 m/s, then will drop back towards the thrower's hand until is returns with a velocity of - 20 m/s. The key point here is that the acceleration, as far as we will be concerned in our problem solving, is ALWAYS -9.8 m/s2.