Final answer:
To score a free throw in basketball, the player must calculate the angle using projectile motion, considering the distance to the basket, the basket's height, and the initial speed of the shot. Practice and understanding the limited room for error due to the hoop and ball sizes are crucial for improving shooting accuracy.
Step-by-step explanation:
To determine the angle at which a basketball player must shoot a free throw to score, we need to analyze the motion using the principles of physics, particularly projectile motion. The player stands at the free throw line, which is 4.57 m (15 ft) from the basket, and aims to throw the ball into a basket that is 3.05 m (10 ft) above the floor. The release height of the ball is 2.44 m (8 ft) and we are given an initial speed of 8.15 m/s.
To solve this problem, we break down the ball's initial velocity into its horizontal (vx) and vertical (vy) components. The time it takes for the ball to reach the basket can be found by using the horizontal component of the motion. We then use the vertical component to determine the angle required for the ball to reach the height of the basket in that time. A larger initial angle is typically preferred by players as it allows a greater margin for error in achieving the correct height.
Professional players improve their shooting accuracy by practicing this technique, among other strategies. They understand that the diameter of the basketball hoop and the size of the basketball leave little room for error, requiring the ball to be precisely on target.