A dart is thrown towards an apple. At the moment the dart is released the apple drops down. We have to determine the angle with the horizontal at which the dart needs to be thrown to hit the apple.
In this problem it should be noticed that there are no details provided except that the apple starts to fall down at the same moment that the dart is released. This gives a hint that the required answer does not depend on any factor like mass of the apple or the dart or the distance between the two.
When the dart is released towards the apple it also is attracted downwards by the same gravitational force of attraction that makes the apple move down. The force acting on each of the objects is proportional to the mass of the object which ensures that the resulting acceleration is the same. The dart should be thrown horizontally towards the apple. As it moves towards the apple, it moves downwards to the same extent as the apple. This ensures that the dart strikes the apple if the speed it is thrown with is sufficient to ensure that it can cover the horizontal distance between the spot it is released from and where the apple falls down from before the dart hits the ground.