Final answer:
To hit a monkey that drops from the tree when a tranquilizer gun is fired, aim directly at it because gravity affects both dart and monkey equally. The monkey's drop does not save it from a bullet since both fall at the same rate.
Step-by-step explanation:
The question pertaining to the tranquilizer gun and the monkey involves a concept in physics known as projectile motion. Specifically, it addresses the effects of gravity on both the tranquilizer dart and the monkey at the moment the trigger is pulled. According to the laws of physics, both the dart and the monkey will begin to accelerate downwards at the same rate due to gravity once the dart is fired and the monkey lets go of the branch. Therefore, the aiming point of the tranquilizer gun should be directly at the monkey, as both the dart and the monkey will fall with the same downward acceleration, and the dart should hit the monkey assuming there are no other external factors (like wind or air resistance) affecting the dart's path.
The monkey's action of letting go of the branch does not save it because the bullet, fired from a rifle with its sights adjusted for gravity, would follow a projectile path that accounts for gravity's pull. So the bullet and the monkey would both fall at the same rate, meaning the monkey would not avoid the bullet by dropping.