according to what you have said , isn't V1 is the velocity of the escaping water ? escaping water has very high velocity , right ?The key here I think is that the effect of the kinetic energy of the water flow is being assumed small enough to be ignored in the calculations.
The velocity of the water in the hose is NOT quoted as being zero,
it is quoted as being NEARLY zero.
Because the boy has pinched the end of the hose, the velocity of the small amount of water escaping will be much higher than the velocity of the water in the hose.
ok , but the author indicate the V1 very near to the escaping point .No, the question does not mention the velocity of the escaping water at all.
V1 is the velocity of the water in the pipe BEFORE it escapes.
This is assumed very low; not zero, but "negligible".
It cannot be zero (otherwise no water would flow at all and so no water would escape).
However because the width of the escaping water jet is small compared to the width of the hose,
the amount of water escaping is not enough to cause much flow in the hose.
Note that the answer indicates that this gives an upper limit to what could be achieved if everything is perfect and all the assumptions are perfectly valid.
However we know that the assumptions are not perfectly valid.
For example, the flow in the hose is not exactly zero (and there is friction and all sorts of other effects that are not included),
so the actual height reached will be less than this simplified mathematical description indicates.
However this less than perfect approximation can still be useful since we know the experimental result will be less than this.
Thus it would be pointless (for example) to try to spray water over somebody on a balcony on the 5th floor.
But you might just reach someone on the 2nd or 3rd floor...
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