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A hot-air balloon plus cargo has a mass of 1890kg and a volume of 11430m^3. The balloon is floating at a constant height of 6.25m above ground. What is the density of hot air in the balllon?

2. Homework Equations :

The force of buoyancy is equal to F=(p_f)(g)(V)

where p_f is equal to the density of the fluid displaced by the object. The force of buoyancy is equal to the weight of the air displaced.

3. The Attempt at a Solution :

Im really stuck. I recognize that for the balloon to be floating at a constant height, the buoyancy force must equal the weight of the balloon.

That is,

(p_f)V=m (gravity cancels on both sides)

Solving this for the density of the air displaced, i get 0.165kg/m^3. Unless if this is the answer and i am really overthinking it, im not sure what aspect of this situation im missing.

I thought that the density found by equating the buoyancy force to the weight is the density of the air outside the balloon.

How does the height of the balloon factor into the equation/situation?

I thought about using the equation P_2=P_1+pgh

but i dont think the atmospheric pressure would vary at a height of 6.25 m.

Im confused.