Final answer:
In soccer, if a ball goes directly into the goal from a corner kick, it is counted as a goal. The possibility of a goalkeeper scoring a goal from a goal kick is a complex physics problem, involving the projectile motion of the ball with an initial speed of 30 m/s over a distance of 95 m. Additionally, a displacement over time graph for a ball kicked to a goalie and back would look similar to one for a hockey puck.
Step-by-step explanation:
If a ball goes directly into the opponent's goal from a corner kick, according to the rules of soccer, the referee should call a goal. This event occurs occasionally in games and is known as an "Olympic goal" or "Gol Olimpico". It is perfectly valid provided it is not touched by another player before entering the goal.
Regarding the physics questions:
Can a goalkeeper score a goal from a goal kick?
In a hypothetical scenario, if a goalkeeper can give a soccer ball a speed of 30 m/s, the goalkeeper might be able to score a goal from their own goal area without the ball touching the ground, covering a distance of about 95 m. This would involve considering factors like air resistance, ball spin, and the angle of projection to determine the feasibility.
Displacement over time graph
The rough sketch of the displacement over time for a ball kicked back to a goalie and returned would resemble the graph of the hockey puck previously mentioned, assuming no external forces like wind or unusual ball behavior affect its motion. The graph typically shows a linear increase in displacement as the ball travels toward the goalie, remains stationary momentarily when it stops, and displays a similar linear increase as it travels back to the player.