Newton 's Second Law in Cartesian Coordinates The sport utility vehicle in , which weighs 3000 lb with its driver. has left the ground after driving over a rise. At the instant shown, the vehicle is moving horizontally at 30 mi/hr and the bottoms of its tires are 24in. above the (approximately) level ground. The earth-fixed coordinate system is placed with its origin 30 in above the ground, at the height of the vehicle's center of mass when the tires first contact the ground. (Assume the vehicle remains horixontal.) Upon first contact, the vehicle's center of mass initially continues moving downward and then rebound upward due to the flexure of the suspension system. While the tires are in contact with ground the force exerted on them by the road is -Ri Nj = -2400i - 18,000yj(lb), where y is the vertical position of the center of mass in feet. (The vertical component N is a funciton of y because of the flexure of the suspension.) When the vehicle hits the ground, what is the magnitude of the maximum acceleration to which it is subjected? If the 160-lb drier is subjected to the same acceleratin what maximum force is exerted on him by the vehicle?