A mass m is projected horizontally along the x-axis with a velocity v towards a second object of mass a m, where 0 < a < 1. If the second mass has a velocity of -2v and the masses collide such that they stick together after the collision. Assuming no external forces are acting, answer the following:
a) Find the expression for the final velocity w after the collision.
b) There exists a value of a such that both masses come to rest after the collision. Prove or disprove.


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