Suppose that you drop a ball from a window 50 metres above the ground. The ball bounces to 50% of its previous height with each bounce. If the ball continues to bounce in this manner how far will it have traveled, up and down, from the time it was dropped from the window until the 25th bounce?

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.