Problem 1.170

A ball moving translationally collides elastically with another, stationary, ball of the same mass. At the moment of impact the angle between the straight line passing through the centres of the balls and the direction of the initial motion of the striking ball is equal to \(\alpha=45^{\circ}\). Assuming the balls to be smooth, find the fraction \(\eta\) of the kinetic energy of the striking ball that turned into potential energy at the moment of the maximum deformation.