Inspired by this tweet,
I decided to do the math and make some pretty pictures to show how angle of release, speed, and air-time relate to each other.
In the first figure, the length of the orange arrows corresponds to the speed of the pitch and the other curves are possible paths that the baseball could follow. If you throw it at a low angle, you have to throw really fast. If you throw at a really high angle, you also have to throw really fast. Somewhere in between is where you would find the minimum throwing speed and it will be close to 45 degrees (not exactly since the ball leaves the pitcher's hand at a different height than it crosses the plate).
In the second figure, the length of the arrows corresponds to the amount of time the ball spends in the air. At a low angle, it spends very little time in the air, but at a high angle, the ball spends a lot of time in the air.
So simple, but so neat.
