For my project I wanted to find the initial velocity of a basketball when shooting foul shots at the free throw line. To begin I started by finding all of my constants; distance, time, acceleration. After I had found my constants i proceeded to come up with an equation. I began the equation with my past knowledge of velocities and how you can use different equations based on what you are trying to find. I used the quadratic formula to better find the correct formula down to the needle. My A value being 1/2a (a being the acceleration), my B value being vox( velocity of x), and my C value being -x (the distance). I was able to compose this down to find vox= -x/t - at/2. I proceeded to set up trials based on my results in the gym with the time being around 2 seconds. I came up with an answer of around 3m/s and then entered this into the cos equation to find the vo of the ball. After it was entered I got an answer of 5.71m/s which when compared to the studies of others, where they received 6-6.3m/s, I came very close to having the prefect velocity.
Down below are different studies done to find the velocity as well and just to better help explain this.