Conservation of momentum, elastic collision problem? Help

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In an elastic collision between two titanium spheres of equal speed, one sphere (300 g) remains at rest after the collision. The momentum conservation equation leads to the conclusion that the mass of the second sphere is one-third that of the first. The derived equation indicates that the velocity of the second sphere after the collision is double the initial speed of the first sphere. This doubling occurs because the first sphere transfers its momentum to the second sphere during the collision. The discussion emphasizes the importance of both momentum and kinetic energy conservation in solving elastic collision problems.
nchin
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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?
 
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This is an elastic collision, so kinetic energy is conserved as well. There are two equations to solve, momentum and kinetic energy.
 

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