(a) [6] An object of mass m₁ moving at velocity u₁ collides elastically with another object of the same mass m₁ initially at rest. Find the velocities v₁ and v₂ of the two balls after collision. (b) [8] Two objects of masses m₁ and m² are moving along the same line. They approach each other with equal and opposite momenta so that the total momentum is zero. Show that, if the collision is elastic, the final speed of each object must be the same as its initial speed. [Remark: The final velocity of each object is not the same as its initial velocity, however.]