A ball is thrown from a rooftop with an initial downward velocity of magnitude vo = 1.9 m/s. The rooftop is a distance above the ground, h = 32 m. In this problem use a coordinate system in which upwards is positive. (a) Find the vertical component of the velocity, ,, in meters per second, with which the ball hits the ground. {b} If we wanted the ball's final speed to be exactly 27.3 m/s, from what height, hnew (in meters), would we need to throw it with the same initial velocity?. (c) If the height is fixed at 32 m, but we wanted the ball's final speed to be 32.7 m/s, what would the vertical component of the initial velocity viy need to be, in meters per second? Vo h y