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butalik [34]
3 years ago
7

A hot air balloon of total mass M (including passengers and luggage) is moving with a downward acceleration of magnitude a. As i

t approaches a mountain, the captain needs to accelerate upwards. He decides to throw enough ballast over board to achieve an upward acceleration of magnitude a/2. What fraction of the initial mass does he have to drop?
Physics
1 answer:
frez [133]3 years ago
5 0

Answer:

When balloon moves in the downward direction two forces acts on it.  

    i) Force exerted by air in the upward direction  

    ii) Weight  

According to newton’s second law of motion:  

      Sum of forces = Ma  

                W – F = Ma  

               Mg – F = Ma     …….. (i)  

when some of the mass m is dropped and balloon is moving in upward direction with acceleration a/2 then,  

               F – W = (M-m)a/2

               F – (M-m)g = (M-m)a/2

               F – Mg + mg = Ma/2 – ma/2 ….. (ii)  

Adding equation (i) and (ii)  

              mg = M(3a/2) – ma/2

              m(g + a/2) = M(3a/2)

              m = M(3a/2)/(g + a/2)

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<em>a</em> = 5.80 m/s²

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