Final answer:
To determine the correct angle above the horizontal for a basketball free throw, one must use the principles of projectile motion. The calculations involve finding the time of horizontal flight and the necessary initial vertical velocity to ensure that the ball's trajectory leads it into the basket when thrown from the free throw line, which is a distance of 4.57m away from a 3.05m high basket.
Step-by-step explanation:
Calculating the Projectile Angle in Basketball
To determine the angle above the horizontal at which the ball must be thrown to hit the basket from the free throw line, we can use the principles of projectile motion. The free throw line is 4.57 m from the basket, and the basket's height is 3.05 m above the floor. The player releases the ball from a height of 2.44 m with an initial speed of 8.15 m/s. We'll need to calculate the necessary initial angle for the ball to follow a trajectory that will lead it to the basket.
To solve this problem, we need to:
- Determine the time it takes for the ball to travel horizontally from the player to the basket.
- Use the vertical motion equations to solve for the time it takes the ball to drop from the release height to the height of the basket.
- Combine these equations to find the angle of release.
The horizontal motion is uniform since there is no acceleration in that direction. For the vertical motion, we must consider the acceleration due to gravity, which is -9.81 m/s2. By setting the final vertical position equal to the basket's height, we can solve for the time of flight and then use this to solve for the necessary initial vertical velocity. Finally, the initial velocity components are used to calculate the launch angle.