Question

You are standing on perfectly slippery ice. You have a tennis racket and a backpack full of tennis balls, and you propel yourself southward by hitting the tennis balls northward against a brick wall. You accelerate fastest when the wall is how far away from you?

Answer 1

Answer:

The distance to the wall does not matter.

Explanation:

According to newton's third law, if you exert a force on the tennis ball to propel it northwards, it will exert equal and opposite force on you to propel you southwards. Therefore, how much you accelerate only depends on how fast you through the balls. And once a ball has left the system ( consisting of you and the ball), it can no longer have an effect on you, so it doesn't matter whether the ball hits a wall nearby or the one millions of miles away.

P.S: all of this is true assuming the balls don't bounce back from the wall and hit you in the face, which would surely give you additional southward acceleration, but it wouldn't be such a pleasant experience!