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.
1) What is the initial speed of the cork, as seen by your friend on the ground?
2) What is the initial direction of the cork as seen by your friend? Give your answer as an angle relative to the horizontal.
3) Determine the maximum height of the cork above the ground.
4) How long does the cork remain in the air?

In the middle of the night you are standing a horizontal distance of 14.0 m from the high fence that surrounds the estate of your rich uncle. the top of the fence is 5.00 m above the ground. you have taped an important message to a rock that you want to throw over the fence. the ground is level, and the width of the fence is small enough to be ignored. you throw the rock from a height of 1.60 m above the ground and at an angle of 54.0 degrees above the horizontal. part a part complete what minimum initial speed must the rock have as it leaves your hand to clear the top of the fence? express your answer with the appropriate units. part b for the initial velocity calculated in the previous part, what horizontal distance beyond the fence will the rock land on the ground?