Section B: Mechanics Whenever a numerical value of g is required, take g = 9.8 m 5-?. 6. Two blocks A and B, of mass 4.5 kg and 1.5 kg respectively, are connected by a light, inextensible string passing over a smooth, fixed pulley. Initially, B is held at rest with the string just taut. B is then released. Calculate the magnitude of the acceleration of A and the tension in the string, stating how you use the fact that the string is inextensible. (7) 7. instantaneously at rest 8. A ball projected from O at u m s" leaves at an angle O above the horizontal. It passes through the point (x, V). 4.9x (1+ tan' 0) (a) Prove that y = x tane- (4) A golfer's ball hit from the ground passes through the point (32, 27.2). If the initial velocity of the ball is 28 m s"]: (b) show that 4tan 0-20tan 0+21 =0 (c) find the two possible angles of projection, and interpret these in context ( 4 ) 9. A plank, AB, of mass Mand length 2a, rests with one end, B, against a rough, vertical tree. The plank is held completely horizontal by a chain, forming a seat. The chain is attached to the plank at A and is attached to the tree at C, which is vertically above B. Amy sits on the plank at D, where DB - d. Amy's mass is 6M. The plank is in equilibrium in a vertical plane that includes the tree. The angle between the plank and the chain is a, where tan a 12 DIT B 2a Model Amy as a particle, the plank as a uniform rod, and the chain as a light, inextensible string. (a) Using the model, show that the tension in the chain is 13Mg (a + 6d) (3) 24a The tree exerts a force on the plank at B whose horizontal component has magnitude - Mg (b) Find d in terms of a (2) The force that the tree exerts on the plank at B makes an angle of S with the horizontal. (c) Find the value of tan B (5) The chain will snap if the tension in it exceeds 6.5Mg (d) Explain how this restricts where Amy can safely sit on the plank. Justify your answer fully. (3)