Endless horses entering a boat
Suppose there is a boat with mass 1 kg, on the boat there are infinetlly many horses with masses 1, 1/2, 1/4, 1/8... kg (Note that there total mass would be 2 kg). The boat starts with velocity 0 m/s and on the water (i.e. there is no friction). If a horse jumps of the boat the boat would get velocity according to conservation of momentum, assume all the horses were to jump of the boat at some order that maximize the boat's final velocity, what would be that final velocity after all the horses jumped from the boat?
Assumptions & Details:
The speed of a jumping horse is 1 m/s.
We assume a horse jumps only in the horizontal direction, such that he doesnt have any momentum in the vertical direction.
Both the boat and the horses have no size (i.e. their volium area and length are 0).
Two or more horses can't jump at once
The answer is 2.
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1 solution
An intresting direction to the problem is that as the number of horses that jumped approaches infinity the speed approaches the speed you were to get if all the horses were to jump at once, this is not trivial and needs to be proven, but gives you a "Shortcut" to the problem