a-research-balloon-equipped-for-atmospheric-studies-is-stationary-at-a-high-alti

Question

A research balloon, equipped for atmospheric studies, is stationary at a high altitude above the Earth's surface. It has a total mass $M_1$ , including both the balloon and attached scientific instruments. For specific data collection, one instrument package, with a mass $M_2$ , needs to be lowered to a different altitude. This instrument package is allowed to slide down a rope at a speed v relative to the balloon. Calculate the velocity $V_b$ of the balloon relative to the Earth immediately after the package starts sliding. What happens to the balloon's velocity relative to the Earth if the instrument stops sliding?

Accepted Answer

$V_{b} = \frac{M_{2}}{M_{1}} v$ ; The balloon stops moving upward.

Answer

$V_{b}=-\frac{M_{2} v}{M_{1}+M_{2}}$ ; The balloon moves downward.

Answer

$V_{b}=-\frac{M_{2} v}{M_{1}+M_{2}}$ ; The balloon stops moving downward.

Answer

$V_{b}=-\frac{M_{2} v}{M_{1}+M_{2}}$ ; The balloon moves upward.