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The Physics of a Toss Machine

For Christmas, my brother got a new baseball toss machine to practice his hitting without having to have a person pitch to him. We went out into the yard to test it out and discovered that finding out where my brother should stand in order to hit the ball was not very easy to do just by sight. The goal is for the ball to fall into the center of his strike zone so he can maximize the force he puts on the ball when the bat strikes and it can go as far as possible. From my knowledge of projectile motion and kinematics, I knew I could help.

My goal was to figure out the distance my brother should stand away from the machine for it to land in the center of his strike zone. From my dad's knowledge about baseball, he was able to tell me that the center of a person's strike zone is the middle of the area from your shoulders down to your knees. In order for my brother to maximize his hitting practice, this is where we wanted the ball to be. My brother is about 5'4 and the center of his strike zone measures to be about 42 inches or 3.5 feet tall.



First, I took a video of the machine just throwing the ball. I knew that I was not going to be able to accurately the velocity of the ball myself because I was missing the acceleration and the angle the ball was being thrown at.




However, I knew taking a video of the ball and using the program Logger Pro could give me the information I was missing. I uploaded the video, entered the meter stick (I do not own a meter stick so I used a tape measure. It is measured to 39.36 in, which google says is equal to one meter), plotted the points of the ball in the video, and graphed that information. By making a line of best fit for each graph, I was able to figure out distances at certain times and the velocity of the ball in the x and y directions.



The velocity can be found from the graph of a linearized distance vs time graph. Logger pro has found this for me. 
*the components of the velocity are not necessary because the program has already taken them into account and done that math for me. 

Here is the information I knew at this point in a kinematics table. 



From logger pro, we can find the delta x and y and the time for when the ball hits the ground, not for when it is in the center of my brother's strike zone. To find the delta x (the distance he should stand away) I needed to do some calculations. 

First, I needed to solve for the time it will take for the ball to be in the center of his strike zone. I did this by using the kinematic equation delta y = 1/2(a)(t^2) + Vi(t) 

Here are my calculations. 


Now, I can use that time and plug it into the same kinematic equation to find delta x. 



I measured out the distance and told my brother to stand about that far away from the machine. Here is the outcome.












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