Hey! Why did you collide when I was resting?

Let $u'$ and $v$ be the post-collision velocities of $m_{A}$ and $m_{B}$ respectively. We require conservation of kinetic energy and linear momentum for this elastic collision according to:

$\frac{1}{2}m_{A}u^2 = \frac{1}{2}m_{A}u'^{2} + \frac{1}{2}m_{B}v^2$ (i)

$m_{A}u = m_{A}u' + m_{B}v$ (ii).

If we solve (ii) for $u'$ and substitute this expression into (i), we obtain:

$\frac{1}{2}m_{A}u^2 = \frac{1}{2}m_{A}(\frac{m_{A}u - m_{B}v}{m_{A}})^{2} + \frac{1}{2}m_{B}v^2$ (iii)

and solving (iii) for $v$ gives:

$v = \frac{2m_{A}}{m_{A}+m_{B}} \cdot u = \frac{(2)(2.5)}{2.5+22.5} \cdot 375 = \boxed{75} m/s.$