# Equation for a falling leaf

1. Sep 10, 2009

### Kaboosh

I've been online searching for interesting stuff about maths and physics.
I came across to this question in yahoo answers that i found quite interesting.

The first equation would be working out how long it takes to reach the ground, and how fast it's going when it arrives. This is actually going to be a differential equation since the air resistance on the leaf will cause it to reach terminal velocity very quickly, and will have the form:

F = mg - k(dx^2/dt^2).

This is the site where i found it.
Code (Text):
Thing is, i have not yet reached to the point where i have learnt or even heard of terminal velocity and integral calculus.
Could somebody please kinda explain it what these things are and how the equation works.
In other words, it's kinda like ''dumbing it down''.

-Kaboosh

2. Sep 10, 2009

### Staff: Mentor

Welcome to PF.

One of the goals of this site is helping people learn how to learn. When you have a question that is so broad that people spend years of their lives studying it, it is tough to get a short answer to a question like "what is calculus?" But the word and concept are something you can type into google or wiki and get concice (though horribly incomplete) answers. So that should always be your starting point. Here's the wiki on calculus:
http://en.wikipedia.org/wiki/Calculus

You should try to read through the whole article.

The answer on that yahoo page also gives a definition of "terminal velocity", but in my words, terminal velocity is the speed an object falls at when the aerodynamic drag drag force equals the weight of the object.

I'm not liking that equation, though. It doesn't look quite right to me. In any case, I prefer the first one here in the wiki for terminal velocity: http://en.wikipedia.org/wiki/Terminal_velocity#Derivation_for_terminal_velocity

It starts the same, with the first term "mg" being the force of the weight of the object and the next term being the drag force. Rather than solving the equations of motion (which requires calculus), you can plug a=f/m, s=at and d=st into a spreadsheet to numerically integrate and find the resulting performance of a falling leaf. This method doesn't require more than junior high math.

3. Sep 15, 2009

Cheers