Final answer:
The answer to whether kickers can advance a recovered free kick in football is no. The question regarding the soccer ball's displacement over time suggests that the graph would generally be similar to that of a hockey puck's motion. For a goalkeeper's kick to reach the opponent's goal over a 95 m distance, physics principles of projectile motion must be applied.
Step-by-step explanation:
The question is related to the physics concept of projectile motion, where the motion of a soccer ball kicked by a goalkeeper is analyzed. To address the student's primary question: Can kickers advance a recovered free kick in football? The simple answer is no, a kicker cannot advance the ball after it is kicked and recovered on a free kick in American football. However, the context appears mixed since the other questions pertain to the sport of soccer, not American football.
Regarding the displacement over time of a kicked soccer ball, if we were to sketch a rough graph of displacement over time for a soccer ball that is kicked 20 m, then stops and is sent back, it would demonstrate an initial increase in displacement, a plateau when the ball stops, and then a second increase as the ball returns. Assuming the context is comparable and we are dealing with similar conditions, yes, the graph is likely to appear similar to a graph depicting the motion of a hockey puck factoring in the time taken for the events to occur, which can affect the slope of the graph during the motion intervals.
For the goalkeeper kicking a soccer ball, if they are able to impart a speed of 30 m/s on the ball, whether it can reach the opponent's goal without touching the ground involves calculations based on projectile motion. These calculations would consider the initial velocity, angle of the projection, air resistance, and gravitational acceleration to determine if the soccer ball can cover the 95 m distance.