An aerostat of mass `m` starts coming down with a constant acceleration `w`. Determine the ballast mass to be dumped for the aerostat to reach the upward acceleration of the same magnitude. The air drag is to be neglected.

Explanation

Let R be the constant upward thrust on the acrostat of mass m, coming down with a constant acceleration `w`. Applying Newton's second law of motion for the aerostat in projection form
`F_y=mw_y`
`mg-R=mv` (1)
Now, if `Deltam` be the mass, to be dumped, then using the Eq. `F_y=mw_y`
`R-(m-Deltam)g=(m-Deltam)w`, (2)
From Eqs. (1) and (2), we get, `Deltam=(2mw)/(g+w)`