Final answer:
Correct option: (b) Both A and B feel that the ball is going down. Observer A on the ground and observer B on the balloon would both perceive the ball as going down after it is dropped from a rising hot air balloon.
Step-by-step explanation:
The correct observation just after the ball is dropped from the balloon moving up with a constant velocity is that both the observer on the ground (A) and the observer on the balloon (B) would feel that the ball is going down. At the moment when the ball is released, it still has the upward velocity it inherited from the balloon. However, since there is no longer any upward force being applied to the ball, gravity will begin to slow it down until it comes to a stop and begins to accelerate downwards. To observer B on the balloon, the ball would immediately appear to start moving downward because their reference frame is also moving upward. To observer A on the ground, the ball might initially appear to ascend very slightly due to its initial velocity, but it will quickly reach its highest point and begin its descent, so it's perceived as having downward motion as well. This concept is similar to other situations analyzed by Galileo, where an object's initial horizontal velocity is retained upon release, and it is the same for different observers, despite the different paths it may appear to take relative to each observer.