Conservation of momentum, elastic collision problem? Help

[nchin]

Two titanium spheres approach each other head-on with the same speed and collide elastically After the collision, one of the spheres, whose mass is 300 g, remains at rest.

What is the mass of the other sphere?

What i did:

m1v1 + m2v2 = m1u1 - m2u2
v1 = 0 b/c at rest

m2v2 = m1u1 - m2u2

m2v2 = (m1 - m2)u

The solution:

v2 = 2u

m2(2u) = (m1-m2)u
2m2 = m1 - m2
3m2 = m1
m2 = m1/3

What I do not understand:

Why is v2 = 2u?? Is it because when m1 collides with m2, it transfers its speed to m2 so then m2 has twice its speed now? So then it's speed is the same as the initial speed times two?

 

[frogjg2003]

This is an elastic collision, so kinetic energy is conserved as well. There are two equations to solve, momentum and kinetic energy.