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$(12$ points$)$ Two blocks $(m_1=m_2=10kg)$ are connected by a string that passes through a massless pulley as shown in the Figure. The first block with mass $m_1$ on a horizontal floor is connected to a spring with spring constant $k=50\frac{N}{m}.$ The spring is initially unstretched and the kinetic friction coefficient between the floor and $m_1$ is ${}_k=0\mathrm{.}25.$ The system is then released from rest and $m_1$ slides along the horizontal plane. Use energy conservation find the speed of the block $m_2$ just before it hits the ground. $)=(10\frac{m}{s^2}$