Final answer:
The theoretical possibility of a goalkeeper kicking a soccer ball into the opponent's goal over a distance of 95 m with a speed of 30 m/s can be calculated using the projectile motion formula. However, real-world conditions like air resistance and elevation changes would impact the feasibility of such a kick.
Step-by-step explanation:
Whether a goalkeeper can kick a soccer ball into the opponent's goal without it touching the ground over a distance of approximately 95 meters depends on the initial speed of the ball and the physics of projectile motion. Given that the goalkeeper can give the ball a speed of 30 m/s, we can calculate whether the ball would reach the opponent's goal based on the principles of projectile motion.
To determine if such a kick is possible, we would use the formula for the horizontal distance of projectile motion: range (R) = (v^2/g) * sin(2θ), where v is the initial velocity, g is the acceleration due to gravity (9.8 m/s^2), and θ is the launch angle.
The maximum range is achieved with a 45-degree launch angle. Without air resistance and assuming an optimal launch angle, plugging the values into the formula shows that it is theoretically possible for the ball to reach the opponent's goal if it is kicked with the perfect angle and initial speed.
However, in real-world conditions, factors such as air resistance, ball spin, and elevation differences between goals would affect the actual distance the ball travels.