After a great deal of experimentation, two Atlantic Institute of Technology senior physics majors determined that when a bottle of French champagne is shaken several times, held upright, and uncorked, its cork travels according to s(t) = -16t² + 40t + 3, where s is its height (in feet) above the ground t seconds after being released.
(a) How high will it go? 

(b) How long is it in the air?