3) when you throw a ball up in the air, the height of the ball is given by the function h(t) = -4.9t2 + vt, where v is the initial speed (in meters per second) with which you threw the ball (we showed this in class). a) prove that the time it takes the ball to reach its maximum height is seconds, and that the total time the ball spends in the air is seconds. 4.9 b) now throw a ball up in the air as hard/fast as you can and with a stop- watch figure out the time the ball spends in the air. then figure out the initial speed with which you threw the ball