Question

An aerostat of mass $m$ starts coming down with a constant acceleration $w$. The ballast mass to be dumped for the aerostat to reach the upward acceleration of the same magnitude is $\Delta m=\frac{xmw}{g+w}$. Find $x$ The air drag is to be neglected.

Answer 1

Let R be the constant upward thrust on the aerostat of mass $m$, coming down with a constant acceleration $w$. Applying Newton's second law of motion for the aerostat in projection form
$F_y=m{w}_y$
$mg-R=mw$ (1)
Now, if $\Delta m$ be the mass, to be dumped, then using the equation $F_y=m{w}_y$
$R-(m-\Delta m)g=(m-\Delta m)w$, (2)
From equations (1) and (2), we get, $\Delta m=\frac{2mw}{g+w}$