Final answer:
The soccer ball reached its highest point, which is 16 feet off the ground, at the midpoint of its horizontal trajectory; thus, it was 20 feet away from the player. Projectile motion principles are used to deduce this information and tackle similar problems in various sports scenarios.
Step-by-step explanation:
Projectile Motion in Soccer
To determine how far from the player the soccer ball reached its highest point, which is 16 feet off the ground, we need to use the principles of projectile motion. The problem implies a symmetric trajectory, meaning the ball will reach its highest point at half the distance of the total horizontal distance traveled if air resistance is neglected. Given that the total distance is 40 feet, the ball would reach its highest point after traveling 20 feet from the player.
A scenario from the question involving a goalkeeper kicking a soccer ball towards the opponent's goal can be also explained using projectile motion. Given an initial speed of 30 m/s and ignoring air resistance, the feasibility of scoring directly from a goal kick depends on the angle of the kick. The optimal angle for maximum range is 45°, but achieving exactly 95 m would need precise control over both angle and initial velocity.
In conclusion, by applying the basic principles of projectile motion, we can solve practical problems involving ball trajectories in sports such as soccer and basketball.