A hot-air balloon rises from the ground with a velocity of 12.00 m/s2ŷ. A champagne bottle is opened to celebrate takeoff, expelling the cork horizontally with a velocity of 15.00 m/s2 x̂ relative to the balloon. When opened, the bottle is 6.00 m above the ground.

(a) What is the initial velocity of the cork, as seen by an observer on the ground? Give your answer in terms of the x and y unit vectors.

(b) What are the speed of the cork and its initial direction of motion as seen by the same observer?

(c) Determine the maximum height above the ground attained by the cork.

(d) For what amount of time does the cork remain in the air?