A car with mass mc$=1020$kg is traveling west through an intersection with a speed of vc$=7\mathrm{.}41$m$/$s when a truck of mass mt$=1590$kg traveling south at vt$=15\mathrm{.}28$m$/$s fails to yield. The vehicles collide, they stick together, and they slide on the asphalt which has a coefficient of kinetic friction of k$=0\mathrm{.}500.$ Associate the positive x direction with east and the positive ydirection with north. How far, in meters, will the vehicles slide after the collision?