# Shooting basketballs into a basketball hoop using projectile motion

1. Jan 11, 2012

### ksafin

Hi,

I need to design a robot that shoots basketballs into a basketball hoop.

My original idea was that the robot will auto-target on the hoop. The hoop has reflective tape around the "square" behind it, which the robot can locate.

Now, when the robot locates this square, it can calculate the height it is from the hoop, the distance lengthwise, etc.

So I was considering using projectile motion to calculate what angle to recline our shooting mechanism at, how much to rotate & in which direction, as well as how fast to fire in the ball, in order to automatically fire and make it into the hoop.

I've taken a general physics course but the projectile motion we learned was more for learning purposes and would be less than accurate if I apply it in this situation.

My question to you, is what equation or set of equations and calculations, should I use to determine all of these factors, taking into account natural factors, of say, air resistance and drag, and excluding external factors such as other robots interfering with the ball mid-flight?

Thanks!

2. Jan 12, 2012

### Staff: Mentor

Welcome to the PF.

The equations that apply are the kinematic equations of motion for a constant acceleration (gravity). Are you familiar with those equations? They are pretty straighforward in their algebraic form. You can learn more about them with a search at wikipedia.org.

EDIT -- to a first approximation you can use the simple equations for projectile motion that you say you have learned already. The secondary corrections will help a little, but really not a lot. A basketball is not retarded by air resistance very much, and to the extent that it is, you can add that in later as you fine tune your shooting percentage.

3. Jan 12, 2012

### ksafin

Sounds good!

Yes I learned the basic algebraic kinematic equations for projectile motions, they were the ones I was referring to.

Sounds good; the ball is only 300 grams, much lighter than an actual basketball; it's actually a foam ball.

So air resistance is almost negligible?

4. Jan 12, 2012

### Staff: Mentor

For a regular basketball, mostly yes. For a lighter ball at 3-point distances, no. But get the shorter shots right first, and then you can add in more complicated shot equations taking air resistance into effect.

I think that the projectile motion pages at wikipedia.org discuss air resistance some, but I'm not sure.

5. Jan 12, 2012

### bigfooted

Air resistance for spheres has been studied for a long time and the equation of motion for spheres is a well studied equation.
There is some information on drag of spheres and their equations of motion here:

I recommend sections 02, 1_1,1_2 and 1_3
Note that it doesn't matter what the size of the sphere is, the equation of motion stays the same (some sections talk about aerosols, which tend to be quite small).

EDIT: I would definitely include drag into the equation, especially when using a lighter ball.