The Beer Keg

In the figure above, somebody has pumped a beer keg with a cross sectional area $A = 0.25$ m$^2$ up to $P = 2$ atmospheres of pressure at the top (1 atm = 10$^5$ Pascals) and pulled the tube off of the tap (which has a cross sectional area of $a = 0.25$ cm$^2$) at the bottom. The surface of the beer is $H = 50$ cm above the tap at the bottom. Fortunately, the keg is up on a stand $h = 1$ m above the ground, so that you can catch it in a bucket.

a) Where should you put the bucket to catch the beer? (Find R. Don't forget $P_0$).

b) How long (approximately) do you have to find a bucket before the beer is all gone?