$1.$ Pushing off: Two ice skaters are standing at rest on ice, which is a frictionless surface. The skaters have masses $50$ kg and $75$ kg$.$ They then push off from each other. Afterwards, the smaller skater is moving to the left at a speed of $2\mathrm{.}6$ m$/$s$.$ a$.$ What is magnitude and direction of the velocity of the larger skater? $[1\mathrm{.}7$ m$/$s to the right$]$ b$.$ What is the change in the total energy of the two skaters? $[+281$ J$]$ c$.$ Where did the change in energy come from? In other words, where was the energy stored before they pushed off? $[$Skaters$$ metabolic energy$]$