Final answer:
To determine the height of the top of the backboard in basketball, we can use projectile motion and follow specific steps based on the given information.
Step-by-step explanation:
The height of the top of the backboard in basketball can be determined using projectile motion. In this case, we can use the information given in the question to solve it. The free throw line is 4.57 m (15 ft) from the basket, which is 3.05 m (10 ft) above the floor. The ball is thrown with an initial speed of 8.15 m/s, releasing it at a height of 2.44 m (8 ft) above the floor.
To solve this problem, we can follow these steps:
- Break down the initial velocity into its horizontal and vertical components.
- Use the kinematic equations to calculate the time it takes for the ball to reach the top of its trajectory and then come back down to the basket.
- Use the time calculated to determine the height of the top of the backboard.
By following these steps, we can determine the height of the top of the backboard.