1. (15 points) A small rubber ball moves between two massive vertical walls, colliding with them. One of the walls is stationary, while the other is moving away from it at a constant speed \( u = 100 \, \text{cm} / \text{s} \). Assuming the ball's motion is always horizontal and the collisions are perfectly elastic, find its final speed if the initial speed of the ball was \( v_{0} = 2017 \, \text{cm} / \text{s} \).
1. With each elastic collision with the moving wall, the direction of the ball's velocity changes to the opposite, and its speed relative to the Earth decreases by $2 u$, i.e., by 200 cm/s. Upon collision with the stationary wall, only the direction changes. Thus, after $n=10$ collisions with the moving wall and the same number with the stationary wall, the ball's speed will become $v=v_{0}-2 u n=17 \mathrm{~cm} / \mathrm{s}$, and the ball will no longer be able to catch up with the receding wall. (15 points)