Final answer:
The shot would not go through the 18-inch hoop if it was aimed towards the center of the basket. The height of the hoop creates an obstacle for the ball, requiring a minimum initial vertical velocity component to clear it. The shot would either hit the front or back of the hoop, or fall short of the hoop.
Step-by-step explanation:
The shot would not go through the 18-inch hoop if it was aimed towards the center of the basket. In order to understand why, we need to consider projectile motion and the height of the hoop. When a basketball is thrown, it follows a curved path due to the force of gravity. This curved path is called a parabola and can be described using projectile motion equations.
When the shot is aimed towards the center of the basket, it means the ball will go directly towards the hoop without any horizontal deviation. However, the 10-foot height of the hoop creates an obstacle for the ball. To clear the hoop, the ball needs to be thrown with an initial vertical velocity component that compensates for the height of the hoop.
Using the known values of the height of the hoop (10 feet or 3.05 meters) and the acceleration due to gravity (9.8 m/s^2), we can calculate the minimum initial vertical velocity component needed to clear the hoop. By setting up the projectile motion equations and solving for the initial velocity in the y-direction, we can find that the ball needs to be thrown with an initial vertical velocity of approximately 7.92 m/s.
Since the initial vertical velocity component needed to clear the hoop is greater than the initial speed of the shot (8.15 m/s), the shot would not go through the hoop. The ball would either hit the front or back of the hoop, or fall short of the hoop.