The Physics of Beating a Confident Goalkeeper

     This week at my younger brother’s soccer game I noticed that a lot of the goalies on the opposing teams were so confident they would play very far out in front of their goals. There was one play where my brother received a back pass and took a chance, lobbing the ball at the goal. His effort was maybe the closest his team had the entire game, and I was curious why the other boys did not seem willing to take a chance when they received a pass back. I wondered if some of the other players were too small to kick the ball half way down the field. It reminded me of elastic collisions and conservation of momentum and how the mass of the player could impact how far they can kick the ball. 

Knowing that the conservation of momentum equation can be arranged such that mballvball + mplayervplayer = mballvball’ + mplayervplayer’ I recognized that some of the boys might not have a substantial enough mass to kick the ball hard enough that its final velocity will allow it to travel all the way to the goal. Since the players have a much more substantial mass than the ball, the player’s velocity will likely not change greatly when they kick the ball. If we consider two scenarios, one where a smaller player kicks the ball and one where a bigger player kicks the ball, we can conclude that if the mass of the ball and it’s initial velocity are held constant, and the players have the same initial and final velocities, that the player with the lighter mass will cause a substantially lower final velocity for the ball. It was interesting to consider how size could be such a big advantage in shooting from a distance.