Question

What is the max distance below the top of the front hoop that supports can be placed?

Answer 1

The angle for a successful free throw in basketball can be determined by applying projectile motion principles, requiring calculations based on the given distances, heights, and initial speed of the throw.

Step-by-step explanation:

Calculating the Angle for a Basketball Free Throw

To determine the angle at which a basketball must be thrown to score a basket from the free throw line, we need to apply the principles of projectile motion. The problem provides the following information: the distance to the basket is 4.57 m, the height of the basket is 3.05 m, the height from which the ball is released is 2.44 m, and the initial speed of the throw is 8.15 m/s.

The steps to solve this include:

1. Breaking down the initial speed into horizontal and vertical components.
2. Using the range equation to find the time it takes for the ball to reach the basket horizontally.
3. Using the time to find the required vertical speed component to ensure the ball reaches the height of the basket.
4. Calculating the angle of projection from the speed components.

The exact calculations are complex and would involve solving quadratic equations that take into account the acceleration due to gravity and the differences in height from release to the basket. As mentioned, players often use a larger angle to allow for a larger margin of error, which simplifies adjustments during the game.