One of the simplest tricks you can use physics for is to figure out how high up you are. Either using a stopwatch or just by counting seconds, drop a dense object (e.g., not paper, a tissue, etc.) and figure out how long (in seconds) it takes from when you release the object to when it hits the ground. Take that number and square it. Multiply it by 16 to get your approximate height in feet, or multiply it by 5 to get your approximate height in meters.
What’s remarkable is that all objects fall at the same rate. All of them. It doesn’t matter what material they’re made out of, how large or small they are, or even whether it’s moving horizontally or not!
There’s only one thing that can screw this up: air resistance. If we were doing this experiment on a planet with no air, like Mercury or the Moon, this method would always work. But Earth has an atmosphere, and if the object you drop is either going too fast or its density is too low, you start running into every falling object’s nightmare, terminal velocity.
Terminal velocity is the speed where the drag force, or the force pushing you up from moving through the air, balances the force of gravity. Fall slower, and gravity will accelerate you up to terminal velocity. Fall faster, and air friction will slow you down to terminal velocity. A human without a parachute in the pencil position falls at around 160 miles per hour (250 kph), while one with a parachute has a terminal velocity of about 15 miles per hour (24 kph).
Now, there is a famous story that goes along with the discovery of the relationship between the distance something falls and the time it takes it to fall. Galileo allegedly went up to the top of the Leaning Tower of Pisa — the tallest building he had available to him — and dropped two different balls off of it; one 10 pound cannonball and one 1 pound ball of the same material.
According to the legend, they hit the ground at exactly the same time. But would they? Let’s figure it out. A 1 pound ball has about 22% of the surface area as a 10 pound ball of identical material, and about 22% of the drag force of the 10 pound ball. But it has only 10% of the force of gravity! This means that as the ball falls farther and farther, the smaller mass ball starts to fall behind, since its drag force is a larger fraction of the gravitational force pulling it down. If we went up to an infinite height, the terminal velocity of the large ball would be 215 mph (340 kph), while the small ball would only reach 145 mph (235 kph).
The Leaning Tower of Pisa is tall — about 55 meters (180 ft) high — but things are moving much slower than terminal velocity. With a little math (it takes some to include air resistance), I can figure out that both balls would have hit the ground after just over 3 seconds of free fall. But not only is there a difference in time, the smaller ball hits the ground more than a quarter of a second later than the large ball! At this height, that means the small ball is over 20 feet behind the large one at impact! It’d be like watching Usain Bolt run a 100 meter race against normal men:
So what do we learn from this? In real life, different balls fall at different rates! It’s the fault of the air, sure, but the tiny little bit of atmosphere we have is enough to totally throw even the simplest physics experiment off! And historically, we can learn that Galileo never actually did this experiment, because if he had, he would have found that his predictions were wrong! In real life, different balls don’t fall at the same rate.
I’ll repeat that: Galileo never actually did his most famous experiment! Go to such great heights and try it for yourself!