a) A car, travelling at an initial speed of 130kmh along a uniform horizontal road. comes to a halt 95 m after its brakes are first applied. The brakes are applied as firmly as possible, without the car ever skidding. (i) Calculate the acceleration during the period that the brakes were applied. (il) Calculate the coefficient of friction between the tyres and road. (iii) Explain whether the answer to part (ii) gives the value of the static or the kinetic coefficient of friction. (iv) Calculate the distance within which the car could be stopped, if the road lay at 12" to the horizontal and the car travelled downhill, but all other details were unchanged. b) A wooden block of mass M = 1.2kg is connected by a light rod of length 0.6m to a frictionless pivot at P. The block is at rest below the pivot when a pro- jectile of mass in = 5.5g is shot horizontally into it 0.6m at speed v. becoming embedded within the wood. Following this event, the rod is measured to deflect by a maximum angle of e = 35 from its initial po- m sition. (i) Derive an expression for the speed of the block plus embedded projectile imme- diately after the collision in terms of m, M and v. (ii) By considering energy conservation, relate the post-collision speed to the max- imum deflection angle, and hence calculate the projectile's speed prior to the collision. (iil) The wooden block is replaced by one of the same mass made of steel, making the projectile collision elastic. Rather than combine with the block, the projectile's direction of travel is reversed by the collision, Calculate the rod's new maximum deflection angle, assuming the same initial projectile speed. [Assume that none of the wood is lost during the collision, and treat the projectile and block as particles.]