Question 3 (25Marks) (LO: 2,3and 4) The roller coaster in the newly opened amtasement park in the Kingdom of Batuain in facing a severe problem and hence it does not stop safely at the end of its joumey. You at a Sorvice Engineer have been asked to design a butfer rpring syntom which has i rubber block of mass 35kg resting on it so that the car of mass 550kg (including passengers) can be stopped anfely at the end of the track. During the trial run it was observed that the car moves at a speed of 65km/h towards tho block which is resting againat a butfer spring and compresses it 500mm before the car comes to complete rest. Assuming the mpring has no initial compression, mass of the spring, air renistance to the motion and stiftness of the rubber block is negligible, calculate the following (a) Common velocity of the car and the block immediately after the impact (7.5Marks) (b) Required stiffness of the butfer spring that will provide the car to stop safely within 500mm of compression. (7.5Marks) (c) The roller coaster car of mass 550Kg is moving around a curve of 40m radius with speed of 15m/s on a level track. Calculate the following: (i) the centripetal acceleration of the car. (5Marks) (ii) the centripetal force. (5Marles)