Answer
See answers.
Work Step by Step
Let the origin of coordinates be the CM of the balloon, gondola, and passenger at rest. The total momentum of the system, relative to Earth, is 0.
The velocity of the passenger with respect to the balloon is -v.
Let the velocity of the balloon with respect to Earth be $v_{BE}$.
The velocity of the passenger with respect to the Earth is $v_{PE}=-v+v_{BE}$.
The sliding mass m does not change the system momentum, i.e., the CM stays at rest. Now use equation 7–10.
$$0=m v_{PE}+M v_{BE}=m(-v+v_{BE})+M v_{BE}$$
$$ v_{BE}=v\frac{m}{M+m}$$
The balloon’s velocity is upward. If the passenger stops sliding, v = 0, and the balloon also stops.