At the start of a basketball game, a referee tosses a basketball straight into the air by giving it some initial speed. After being given that speed, the ball reaches a maximum height, above where it started. Using the conservation of energy, find expressions for (a) the ball's initial speed in terms of the gravitational acceleration, g and the maximum height and (b) the height of the ball when it has a speed v in terms of its current height y, the gravitational acceleration g and the maximum height .
