A balloon of total mass 840 kg is rising vertically with constant speed. As a result of releasing some ballast, the balloon immediately accelerates at 0.5 m/s². Calculate the mass of the ballast released.

Answer 1

Firstly, when the balloon is moving uniformly,
the buoyant force F is equal to the gravity
F = m•g.
After the ballast releasing,
the buoyant force F isn’t changed
because it is equal to the weight of the air
displaced by the balloon.
Now the equation of the balloon motion is
(m-Δm) •a = F – (m - Δm) •g = m•g– (m - Δm) •g,
Δm = m•a/g-a = 840•0.5/(9.8-0.5) = 45.16 kg.