Two springs with a spring constant k$1=10\mathrm{.}0$N$/$m and k$2=20\mathrm{.}0$ N$/$m face each other across a frictionless surface. A puck of mass $500$g moves with a speed of $1\mathrm{.}4$ m$/$s towards spring $1.$ After compressing spring $1$ and being released, the puck moves towards spring $2,$ eventually colliding with it and compressing it$.$ Find the maximum distance delta x$2$ that spring $2$ is compressed from its rest length