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What is the water speed as it leaves the nozzle?

  1. Oct 11, 2014 #1
    1. The problem statement, all variables and given/known data

    nGlQqa.jpg

    Suppose you adjust your garden hose nozzle for a hard stream of water. You point the nozzle vertically upward at a height of 1.5 m above the ground. When you quickly turn off the nozzle, you hear the water striking the ground next to you for another 2.0 s.
    What is the water speed as it leaves the nozzle?


    2. Relevant equations

    vavg = Δx/ Δt
    vfinal2 =vinitial2 + 2ax


    3. The attempt at a solution

    b46Vdn.jpg
    From the vavg equation:
    vg = 1.5/2t + 10t
    v0 = 1.5/2t - 10t

    From the other equation

    http://www4a.wolframalpha.com/Calculate/MSP/MSP10431h9ic8g7736e702600003bb73a2eg362c825?MSPStoreType=image/gif&s=34&w=238.&h=35. [Broken]

    http://www4a.wolframalpha.com/Calculate/MSP/MSP38881h9ic4fc19b732c400004f1gdedhga6cgg3b?MSPStoreType=image/gif&s=34&w=38.&h=18. [Broken]
    http://www4a.wolframalpha.com/Calculate/MSP/MSP38851h9ic4fc19b732c400002b4de3h0dg0716h1?MSPStoreType=image/gif&s=34&w=49.&h=18. [Broken]

    v0 was (1.5/2t - 10t).
    So it becomes 0.75 - 10 = -9.25.

    I think my answer is correct because I've come across the value of 9.25 on some other topics too. I'm not asking for a value correction. But what I found is minus 9.25 while others claim it is plus 9.25. Is this because of the direction of the water? Also, what about the spots I wrote (1-t). Have they simply become zero?
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Oct 11, 2014 #2

    haruspex

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    You wrote 1.5/2t when you meant 1.5/(2t), then used it as though it wss (1.5/2)t. t cannot possibly be 1; look at the 1-t in your diagram.
    There's a much quicker way. You have the time from the last drops of water leaving the pipe to hitting the ground, you have the acceleration, and you have the net change in height. One SUVAT equation will relate these to the initial velocity.
     
  4. Oct 11, 2014 #3
    Thanks for pointing out the silly mistake. This, unfortunately, was the first way to come to my mind. I'd better think more. :D
     
  5. Oct 11, 2014 #4
  6. Oct 11, 2014 #5

    haruspex

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    To that many digits, yes.
     
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