Problem 3: (10 points) The impatient driver of vehicle 1 enters a highway from a ramp when vehicle 2 is on the highway approaching the intersection. When the driver of vehicle 2 notices that vehicle 1 is on the highway traveling at a low speed, the separation between the rear of vehicle 1 and the front of vehicle 2 is d and the speeds of both vehicles are given as voi and Vo2- If the road has a grade G, the acceleration of vehicle 1 is ai, the perception-reaction time of the driver of vehicle 2 is 8, the coefficient of friction between the tires of vehicle 2 and the pavement is fand both vehicles are constrained to stay in the same lane, determine: a) The acceleration rate in ft/s of vehicle 2 (i.e., az) while braking (use the practical equation that contains the term f). b) Find if the vehicles collide. If they do not collide find the minimum separation and the speeds of the vehicles at the instant of minimum separation. If they collide, find the position x at the instant of collision and the speeds of both vehicles at that instant (Set x = O as the initial position of vehicle 2 as shown in the time-space diagram below). Position x Vehicle 1 d VO2 Vehicle 2 Timet Problem 3: (10 points) The impatient driver of vehicle 1 enters a highway from a ramp when vehicle 2 is on the highway approaching the intersection. When the driver of vehicle 2 notices that vehicle 1 is on the highway traveling at a low speed, the separation between the rear of vehicle 1 and the front of vehicle 2 is d and the speeds of both vehicles are given as voi and Vo2- If the road has a grade G, the acceleration of vehicle 1 is ai, the perception-reaction time of the driver of vehicle 2 is 8, the coefficient of friction between the tires of vehicle 2 and the pavement is fand both vehicles are constrained to stay in the same lane, determine: a) The acceleration rate in ft/s of vehicle 2 (i.e., az) while braking (use the practical equation that contains the term f). b) Find if the vehicles collide. If they do not collide find the minimum separation and the speeds of the vehicles at the instant of minimum separation. If they collide, find the position x at the instant of collision and the speeds of both vehicles at that instant (Set x = O as the initial position of vehicle 2 as shown in the time-space diagram below). Position x Vehicle 1 d VO2 Vehicle 2 Timet