A novelty toy has two spheres of equal mass suspended by strings of equal length and negligible mass, and arranged so that the spheres can collide head-on at the bottom of each string’s swing. One sphere is given an initial velocity u towards the other, which is at rest hanging vertically. A collision between the two spheres has a coefficient of restitution e, which is less than 1. After a collision the spheres swing on the strings until they collide again. You may assume that the amplitudes of the swings are small and that swinging is frictionless. Under these conditions the spheres will collide again at the bottom of their swings with exactly the same speeds as they had just after the previous collision, though the direction of their velocities will have reversed. 1.Investigate the sequence of speeds at successive collision for each of the spheres, by tracking the calculations through a few collisions. You should be able to detect a pattern emerging. To simplify your calculations you might express velocities in units of u. 2.What is the ultimate velocity of each of the spheres? 3. How much of the the original kinetic energy is ultimately lost in the collisions?