A scientist wants to determine the rate of water flow over a small waterfall after a storm. They find a 10 cm wide board. They rest the center of the board on a large rock rising out of the pool of water below the fall, allowing it to pivot up and down. The scientist, who has a mass of 70 kg , sits at one end of the board and finds that the board remains horizontal, and balanced about the pivot, if the other end of the board is inserted 4.0 cm into the waterfall (i.e. such that the falling water strikes a 40cm^(2) area at the end of the board). In the following, you can assume that all the water strikes the very end of the board, that it does not splash upward when it hits, and that it flows off immediately without pooling on the board.
a) Given that the density of water is 1000(kg)/(m^(3)), what is the speed of the water striking the board?
b) If the sheet of falling water at the base of the fall is 2.0 m wide and 0.10 m thick, what is the total volume rate of falling water (in ((m^(3))/(s)))? What is the mass of water going over the fall in 1 minute?