Question

Suppose that a passenger intent on lunch during his first ride in a hot-air balloon accidently drops an apple over the side during the balloon

Answer 1

-Notice that the acceleration of the apple in a balloon frame of reference is:

a (apple) = g + a(balloon) = 9.8m/2² +4m/s²=13.8m/s since the apple will aproach faster towards the balloon cabin as it is beeing atracted by the earth gravity itself and also the balloon is accelerating towards the apple. So these 2 efects combine to make the apple approche faster not unly due to gravity but also because the balloon is accelerating upwards.

-The apple is moving upwards with respect to the ground, but it is movind downwards with respect to the balloon itself as initially these two were moving upwards at 2 m/s and then the balloon acelerates and the apple is dropped inside the balloon.But keep in mind that for an observer on the ground, the apple continues its motion vertically up since at the moment of releasing, this apple is going upwards with the balloon together at 2m/s.

-The apple increases its speed with respect to an observer in the balloon but the speed decreases with respect to an observer standing on ground.

I hope it can be clearer now for you my dear student. Good Luck with that.