I am not sure If you know how many physicists are watching baseball, there are actually many. I think it is so popular among us because there are some very basic principles at work. You can model the movement of a simple flying ball in an introductory course, but you can also make it more complex (and interesting). So, with this in mind, let us consider the following questions: How do baseball players catch the flyball?
When the batter hits the ball, it can sprint in the air for three to six seconds and then fall into the outfield. This allows outfielders only time to calculate their landing position. Do you think they will pull out a textbook and look up the equation of the projectile motion? never.But the player Yes Use physics. This is what happened.
Catch the ball in the way of physics textbooks
First, let me use physics to find the landing position of the ball. After that, I will solve this problem according to the way players play in the actual game.
But let us make two assumptions about this ball. First of all, there will be no air resistance on it. (It will be easier to calculate without air resistance. In addition, in many cases where the ball speed is low, this approximation is quite reasonable.) Second, I will make this two-dimensional (rather than 3D). The ball will be shot in a straight line directly to the player on the field. In this way, I don’t have to worry about players moving left and right in order to catch the ball, just back and forth.
There are many variables in this question, so let me start with a graph showing all these quantities. I will assume that the ball is launched from the origin so that it travels along the x-axis.
There are many things here, so let us describe each variable.
- v0 Is the starting speed of hitting a baseball.
- θ is the launch angle of the ball.
- Xphosphorus Is the starting position of the player (along the x axis).
- resistance Is the final x position of the baseball when it returns to the ground.
- Finally, there are vectors r. This is the vector from the position of the player to the position of the ball (in the air). Angle θB Is the angle of this vector relative to the ground.