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Compute all given parts of following problem:
Problem: You are in a hot air balloon (yes, another balloon problem!) rising from the ground at a constant velocity of 3.00 m/s upward. To celebrate the takeoff, you open a bottle of champagne, expelling the cork with a horizontal velocity of 6.70 m/s relative to the balloon. When opened, the bottle is 6.50 m above the ground.
Part A: What is the initial speed of the cork, as seen by your friend on the ground?
Part B: What is the initial direction of the cork as seen by your friend? Give your answer as an angle relative to the horizontal.
Part C: Determine the maximum height of the cork above the ground.
Part D: How long does the cork remain in the air?
Please clarify the equations and steps are used to get the answer. Thanks!
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