(Originais Teachy 2023) - Questão Muito Difícil de Educação Física

Imagine a scenario where the rules of football have been modified to incorporate principles of physics, such as the conservation of momentum. In this modified game, players are allowed to use a new type of ball that has a variable mass. The mass of the ball can be increased or decreased during the match by a mechanism installed in the ball. The mechanism works in such a way that the total momentum of the ball and the player kicking it remains constant before and after the mass change. If a player kicks the ball at a certain velocity and the mass of the ball is doubled just before the kick, the ball will leave the player's foot at half the original velocity. Knowing that the original mass of the ball is 0.5 kg, the player's foot applies a force that accelerates the ball uniformly from rest to its original velocity in 0.2 seconds, and the new mass after the increase is 1 kg, calculate: 1) The original velocity at which the player's foot kicked the ball. 2) The final velocity of the ball after the mass increase if the ball is kicked again by the same player's foot with the same force and in the same time interval as the original kick. Consider the force applied by the player's foot as constant during the time of acceleration and neglect the effects of air resistance on the ball.