You are in a hot air balloon (yes, another balloon problem) rising from the grou

Question

You are in a hot air balloon (yes, another balloon problem) rising from the ground at a constant velocity of 2.80 m/s upward. To celebrate the takeoff, you open a bottle of champagne, expelling the cork with a horizontal velocity of 6.30 m/s relative to the Balloon. When opened, the bottle is 7.90 m above the ground. What is the initial speed of the cork, as seen by your friend on the ground? What is the initial direction of the cork as seen by your friend? Give your answer at an angle relative to the horizontal. Determine the maximum height of the cork above the ground. How long does the cork remain in the air?

Explanation / Answer

initial direction as seen by frnd

1) Tan-1 ( 2.8/6.3) = 0.418 radians with horizontal

2) Maximum height of the cork

= 7.9 + 2.82/2g

= 8.3 m

3) t = root ( 2xs/g)

=1.3 seconds

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