Two spheres of mass $1$ kg and $1\mathrm{.}5$ kg hang from the ends of two $1\mathrm{.}5$ meter long threads fixed at the ceiling point. The lighter sphere is pulled to one side so that its thread forms an angle of $60$ degrees with the vertical. This sphere is released and they collide.

 $1.$ With what speed does the lighter sphere collide?

 $2.$ What speeds does each sphere acquire after the collision.

 $3.$ What angles do the spheres acquire after the collision when their velocities are zero?