You are driving north through an intersection in a 55 $mi/hr$ speed zone, when the local chief of police, who is driving his new cadillac and approaching the intersection from the west, hits you broadside. the two cars stick together and skid a distance 35.9 $m$ with locked wheels at an angle of 66.8° to the east of north. the mass of your car is 1415.0 $kg$ while the cadillac has a mass 1905.0 $kg$. the coefficent of sliding friction is 0.80. the chief of police is angry that you have damaged his new cadillac and gives you a ticket for speeding. the local judge is going to believe his chief of police rather than some out-of-town student. you realize that the knowledge you learned in your physics course is your only hope for acquittal. compute the speed of the chief of police immediately prior to the collision.