Ahot-air balloon consists of a basket hanging beneath a large envelope filled with hot air. a typical hot-air balloon has a total mass of 534 kg, including passengers in its basket, and holds 2.77 ✕ 103 m3 of hot air in its envelope. if the ambient air density is 1.23 kg/m3, determine the density (in kg/m3) of hot air inside the envelope when the balloon is neutrally buoyant. neglect the volume of air displaced by the basket and passengers. hint kg/m

  = 1,037 kg/m³

Explanation:

This is a problem with the Archimedes principle that states that the thrust on a body is equal to the weight of the dislodged fluid.

Let's write Newton's second law for this balance

     B- W- = 0

     B = W +  

Where W is the weight of the basket and the passengers and Wair is the weight of the air inside the balloon

The thrust is

     B = g V

We replace

    g V = mg + g V

    = ( V - m) / V

    = - m / V

    = -m / V

  = 1.23 - 534 /2.77 103

  = 1,037 kg/m³

acceleration = (change in speed) / (time for the change)

change in speed = (20-120)= -100 m/s.

1.5 min = 90 sec

acceleration = -100/90 = -1.11 m/s^2.

we don't care about the 150kg or the 2,500 meters. they don't make any difference.

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