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Homework Help: Can this formula be used to solve this?

  1. Jan 30, 2010 #1
    1. The problem statement, all variables and given/known data

    Firemen are shooting a stream of water at a burning building using a high-pressure hose that shoots out the water with a speed of 27.5 m/s as it leaves the end of the hose. Once it leaves the hose, the water moves in projectile motion. The firemen adjust the angle of elevation Θ of the hose until the water takes 3.00 s to reach a building 51.81 m away. You can ignore air resistance; assume that the end of the hose is at ground level.

    How fast is it moving just before it hits the building?

    Θ=51.1

    2. Relevant equations

    The equation i used to solve it was V=sqrt(vx2+vy2) and the answer was found to be 19.0 m/s

    i was wondering if this equation would work to solve it? i cant get it to come out with 19 m/s though.

    Vf2= Vyi2+2(ay)(Δy)

    3. The attempt at a solution

    Vf2= Vyi2+2(ay)(Δy)

    so with this equation i used Vyi to be 27.5sin(51.1)=21.01

    i used ay to be -9.8

    i used Δy to be 27.5sin(51.1)(3) + .5(-9.8)(32) = 20.11 - 0 = 20.11
    (the minus 0 is because of the final height minus the initial height).


    Vf2= Vyi2+2(ay)(Δy)

    Vf = 6.87 which is definitely wrong.

    Anyone know why this equation doesnt work using these numbers i calculated?

    Any suggestions. Thanks :)
     
  2. jcsd
  3. Jan 30, 2010 #2

    Doc Al

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    Staff: Mentor

    That will find Vyf, not the complete Vf. You still need to add Vx to get the total V.
     
  4. Jan 30, 2010 #3
    if i add that to the Vx then that comes out to be 24.14 m/s which is also not the correct answer.

    6.87 + 27.5cos(51.1) = 24.14 m/s
     
  5. Jan 31, 2010 #4

    Doc Al

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    Staff: Mentor

    These are vector components. When I said 'add' I meant combine them like vectors:
     
  6. Jan 31, 2010 #5
    oh i see what you are saying.

    well i did that and its still a little under

    sqrt(17.27^2 + 6.87^2) = 18.58 :(

    i guess this way may just not work.

    Thank you for your help and explanations.
     
  7. Jan 31, 2010 #6

    Doc Al

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    Staff: Mentor

    It should work just fine. Check your arithmetic. For example, this calculation is not quite right:
     
  8. Jan 31, 2010 #7
    thank you. with that new number of 21.4 it works out correctly.

    thank you for catching that error and all of your time and help :)
     
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