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You have had a lot of debates on the final position
of boatman's boat.
There are many factors that will have impact on this.
Basically, they are:
1. The speed of the boat;
2. The aera of the boat that in the water;
3. The structure or the shape of the boat;
4. The dynamic resistance of the water;
5. The static resistance of the water.
For this problem, the momentum k Xj
and momentum k Xl = k (Xl1 + Xl2) are
momentum lost during jump and landing,
They are necessary by the momentum
conservation theorem, caused by the speed
of the boat and can not be ignored. This is
the first type of dynamic force, converted
partially into second dynamic energy.
If the boat return, it will overcome the extra
second type of dynamic resistance caused
by the water flow energy from the initial
movement of the boat, which will reduce
the speed of boat return.
Dynamic resistances will always consume
energy and prevent boat return.
Static resistance may prevent the boat return
if it big enough compared with 'return
momentum' or prevent the boat move at all.
So the boat will never return even in ideal
condition.
Energy is always conserved.
This problem can use any type of energy
conservation theorem.
Energy conservation theorems have many
different types and formats, they can be proved
by using many different techniques.
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