Hole in the Bucket Problem

  1. 1. The problem statement, all variables and given/known data
    This was a problem on a test today, and it is driving me nuts that I cannot figure it out. We were told that we had a bucket 1 meter off of the ground with a 3.5 mm hole in the bottom. The water sprayed a horizontal stream 60 cm from the bucket. We are asked to find the


    2. Relevant equations
    I know we need to use bernoulli's just not sure how.


    3. The attempt at a solution
    I tried to solve for velocity and height.. but it seems like you need one to get the other.
     
  2. jcsd
  3. gneill

    Staff: Mentor

    Find the... ???
     
  4. haruspex

    haruspex 12,790
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    How long will the water take to hit the ground? If it lands 60cm away, how fast is it moving horizontally?
     
  5. Oh sorry asked to find the height of the water in the bucket
     
  6. gneill

    Staff: Mentor

    Start with haruspex's advice. If you consider the water stream to be composed of a series of discrete slugs of water, each behaving like a free-falling projectile, can you determine the initial horizontal velocity one such slug must have in order to land 60cm away?

    After that you can worry about how deep the water in the bucket has to be to produce this velocity (as you surmised, Bernoulli is involved).
     
  7. horizontal distance

    I cannot seem to find a way to find the time it takes to hit the ground, when all I know is distance in the y and x direction. Is acceleration g? and if so does that mean it's zero in the x?
     
  8. gneill

    Staff: Mentor

    Yes, the water is falling under the influence of gravity. So how long does it take something to fall 1m from rest?
     
  9. I found the right equation. Solved for t in the y direction and then used that to find initial v in the x direction, then used bernoulli's to find height! Thanks you guys very much for the help!
     
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