Physics: ball launch using gravity

[JoeXIII'007]

It's been a while since I posted here, but a few things have changed with the project, which is working quite well. First, here's the criteria for the ball launcher from the sheet my physics teacher gave:

Build a machine that will project a ball (current weight is roughly 30-40 grams, it is no longer 10) through a hoop that is ~ 10 cm wide, 1 meter in the x direction, and 1 meter in the y direction.

Rules:

• you will have three tries to get the ball through the hoop.
• The ball must move at least 1 meter in the +x direction once it leaves the bounds of the machine.
• Calculations to support your design must be completed in report form. Include the following in the calculations:
  • Force of the mechanism acting on the ball.
  • Graph showing the path of the ball once it leaves the mechanism.
  • Speed the ball is traveling through the air

Grades will be determined by the accuracy of calculations and physics

• 50pts Mechanics of the machine (does it work)
• 35pts Creativity of the design
• 15pts Extra points may be earned for distances traveled through the air > 1 meter.

So, here's the status of the project, which is due next Wednesday. I have it launching the ball 10-15 cm short of the 1 meter height and 1 meter away requirement. HOWEVER, I have been able to consistently get the ball through the hoop, which is in vertical orientation, between 84-94 cm high. The angle, which I am yet to measure is about 45-55 degrees. Do not trust the protractor like device in one of the pics, for I do have the ramp a bit higher than 45.

The device consists of a vertically standing PVC pipe that is 1.9 meters long. It provides the ball gravity acceleration. At the end of the pipe, I have 2 'hot-wheels' flexible tracks that end about .75 horizontal meters away, pointing the ball 45-55 degrees to the hoop.

I need to know how exactly to measure the curve, circular or not. It was never drafted, and was tweaked SEVERAL times that any rough/initial draft with any accuracy would be no longer accurate. Pictures are attached of the device, or should I say ramp.

As far as calculations are concerned, I know that I can get the speed and force before the ball hits the curve using v = gt and f = ma respectively since it's a relatively straight vertical drop. It's the curve that I need measured, and the angle I can get easily.

Thanks again, and any ideas on how to get the ball just a wee bit higher would be really great.

-Joe