AX-kg bucket is lifted from the ground into the air by pulling in Ym of rope at a constant speed. The rope weighs P kg/m. a)Write a mathematical expression to

calculate the amount of work needed to rise the bucket to a distance h (top of the building shown, in meters). [5 marks] b)Given X =3, Y =h = 9, and P = 0.15. How much work was spent lifting the bucket and rope? [5 marks] Assume now the bucket is leaking. It starts with 10 L of water and leaks at a constant rate. It finishes draining just as it reaches the top. How much work was spent lifting the water alone? Do not include the rope and bucket. (Hint: find the proportion c)of water left at elevation x m.) [5 marks] Some workers changed to a larger bucket that held 25 L of water, but the new bucket had an even larger leak so that it, too,was empty by the time it reached the top. Assume that the water leaked out at a steady rate. d) How much work was done lifting the water alone? (Do not include the rope and bucket.) [5 marks)