How to determine the point at which you can catch the ball?

Question

Linear algebra

How to determine the point at which the player (football player) will be able to catch the ball in advance?
It is known: the position of the player, the maximum acceleration, the current position of the ball (xb,yb) and its expected position at the next iteration (in a unit of time t)
How to find the point where the player can be and be at that moment on the path of the ball?

Answer 1

well, you first need to describe the movement model for the ball and the player (knowing their parameters, speed, acceleration, initial coordinates),
then express the predicted coordinates in terms of the velocity vector multiplied by the time,
then solve the general system of linear equations,
roughly speaking:
unknown final coordinate of the ball = vector speed of movement for sword * time of movement of the ball
unknown final coordinate for the player = vector speed of movement of the player * time of movement of the player
----------- by
varying the unknown parameters (time, and direction of movement) you can find the conditions under which unknown coordinates for the sword and the player are the same (provided that the movement time is equal).
You can have many solutions, choose the one that allows you to minimize the time parameter for the meeting of the ball and the player.