Suppose that an air cannon in the Punkin Chunkin contest whose muzzle is 5 feet above the ground fires a pumpkin at an angle of 45 to the horizontal with a muzzle velocity of 303 feet per second. The model s(t)=-16t +208t+5 can be used to estimate the heights of an object after t seconds. (a) Determine the time at which the pumpkin is at a maximum height. (b) Determine the maximum height of the pumpkin. (c) After how long will the pumpkin strike the ground?