Well, I can't seem to get my mind off this thing. I mean it's really simple and yet I find myself considering and reconsidering materials, configurations, issues ... it's a flaw I have. I actually get more done when I don't have much time and I'm shooting from the hip. I can make things work versus engineering them to (that's my take anyway). So yesterday I spent my lunch rediscovering the formulas for projectile motion.
When a ball is launched at an angle (theta) the only force acting in the x direction (horizontal) is the initial force that propels the ball in the x direction. But the y direction has gravity that works against it. My thinking was that I know the height and range from the hoop. At what angle and what linear speed would the ball have to be shot to hit this point at it’s apex (upward velocity = 0)?
I created a spreadsheet to play with different angles to determine the velocity of the ball. Then using the calculated values, I plugged these back in and plotted the flight path with respect to time. I added a vertical line to show the hoop. In this way I can actually change the angle, initial velocity and launcher height to see the trajectory and time to target. Have a look below.
In addition, I calculated the RPM of the motor for the specified velocity and then reversed it to specify the motor speed to calculate the linear velocity so I could play with the angle. It’s quite useful, but we’ll see how reality plays out.
Onward,
Jay
