To determine the optimal angle for a basketball player to throw a ball into a basket, the player, standing 10m away and 2m tall, must account for the basket's height of 3m. The initial speed of the throw is 11m/s, leading to calculations involving both horizontal and vertical motion components. The equations for maximum height and range are not sufficient due to the differing heights, necessitating a new approach that separates the x and y components of motion. The discussion emphasizes solving for the time it takes to reach the basket horizontally and using that to find the vertical height at that time. Ultimately, the calculations lead to an optimal angle of approximately 35.294 degrees for the throw.