Consider a large tank filled with a liquid that has a density p. The tank is a cylinder with radius R, and the surface of the liquid is a height H above the ground. There is no lid on top of the tank, so it's open to the air. H V On the side of the tank there is a circular hole with radius r, and this hole is at a height h above the ground. The liquid shoots out of this hole and hits the ground a distance x from the foot of the tank. R x For all the questions below, give your answer in terms of the variables p, R, H, r, h, and g only. Don't leave your answer in terms of any other variables. (a) Show that the speed v of the liquid coming out of the hole is given by v = 2g(H-h) 1-r4/R4 (b) If the width of the tank is much larger than the size of the hole, then R r and we find that the above formula simplifies to v = 2g(H h). For this situation, determine how the range x depends on the location of the hole, h. (c) What is the range x of the liquid, if the hole is near the ground (h0)? Explain in words why this range is so small. (d) What is the range x of the liquid, if the hole is near the top of the tank (hH)? Explain in words why the range is so small. (e) Determine for what h we would get the largest range x. Assume that the tank is much wider than the hole (R >> r).