Help calculating force needed for a robot's basketball shot

[Truffle98]

Summary:: I'm on a high school robotics team and this year one of the challenges is to have a robot that can pick up balls and shoot them into a large bowl about 9 feet above the ground. We are planning on using flywheels to launch this ball, which we will also have to figure out how to give the proper momentum. The robot will be able to detect its distance away from the top of the bowl and should be able to calculate force needed from wherever it picks up a ball.

So, this robot will have a limelight sensor, which it will be able to see reflective tape around the rim of the bowl, so it will be able to calculate how far it is from said bowl using the angular size formula. Using this distance, I want to be able to shoot the ball from the robot and make the shot into the bowl every time. I will include dimensions in a second. Is it possible to make this shot, assuming it is not obstructed by any other part of the bowl's structure, using the same launch angle? If it is not possible to use the same launch angle every time then that is ok, I just wanted to keep it simple. We will be using flywheels to launch the balls, and hopefully we will be able to be fairly consistent with the force we give them, but if anyone has other ideas on a mechanism powerful and accurate enough for this challenge, please let me know. Otherwise, if you know how to be consistent using flywheels, I am also curious to hear your insight.

Dimensions:
Bowl height: The lip of the bowl is 8 ft 8 inches off the ground.
Bowl radius: The bowl has a radius of 2 ft.
Ball size: It is a sphere that has a radius of 4 3/4 in.
Ball weight: 9 1/2 oz, with 3 1/2 psi.

There are more details in this manual regarding the competition, read more here.

I do not know much about physics, so if there's anything I am misunderstanding or if more details are necessary, please let me know and I will get back to you.

 

[Office_Shredder]

You probably can't use the same launch angle every time. If you're really close to the rim, you need to shoot up at a very high angle, and if you're far from the rim, you will probably hit the ceiling trying to shoot at the same angle. Maybe if you only have to shoot from sufficiently far away

 

[Svein]

Firstly you need to determine the parabola that starts at the robot and ends up in the basket. You will need an additional parameter - you choose it.
Then you must calculate the angle of which to launch the ball and the force needed to throw the ball to the top of the parabola.
There you are - simple mathematics and simple physics.

 

[fresh_42]

At top of the parabola, the ball has a certain potential and kinetic energy. The sum of these must be achieved by the acceleration of the ball during the way the robot arm applies this acceleration:
$$
mgh+\dfrac{1}{2}mv^2=ma\cdot w
$$

 

[berkeman]

Summary:: I'm on a high school robotics team and this year one of the challenges is to have a robot that can pick up balls and shoot them into a large bowl about 9 feet above the ground. We are planning on using flywheels to launch this ball,

(thread moved to the schoolwork forums)

Welcome to PF, @Truffle98

I don't think I'd use flywheels to lauch the ball -- it seems like it would be pretty hard to get consistent launch velocities and no sideways spin (due to friction and compression issues). Instead, I'd be thinking more along the lines of an adjustable catapult-type launcher. I'd probably make the forward stop point variable to change the launch angle, and the sping-loaded back point adjustable to be able to adjust the exit velocity from the catapult launcher...