What is the Velocity of Water Exiting a Hole in a Bucket?

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In summary, the water moves horizontally at a speed of v=60cm/s. It takes t=1.5s for the water to hit the ground and land 60cm away.
  • #1
HelpMePleez
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Homework Statement


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


Homework Equations


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


The Attempt at a Solution


I tried to solve for velocity and height.. but it seems like you need one to get the other.
 
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  • #2
HelpMePleez said:

Homework Statement


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
Find the... ?
 
  • #3
How long will the water take to hit the ground? If it lands 60cm away, how fast is it moving horizontally?
 
  • #4
Oh sorry asked to find the height of the water in the bucket
 
  • #5
HelpMePleez said:
Oh sorry asked to find the height of the water in the bucket

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).
 
  • #6
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?
 
  • #7
HelpMePleez said:
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?
Yes, the water is falling under the influence of gravity. So how long does it take something to fall 1m from rest?
 
  • #8
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!
 

What is the "Hole in the Bucket Problem"?

The "Hole in the Bucket Problem" is a mathematical puzzle that involves a bucket with a hole in it and how to fill or empty the bucket using only certain tools and actions.

What is the goal of the "Hole in the Bucket Problem"?

The goal of the "Hole in the Bucket Problem" is to determine the most efficient way to fill or empty a bucket with a hole in it using only certain tools and actions.

What tools and actions are allowed in the "Hole in the Bucket Problem"?

The only tools and actions allowed in the "Hole in the Bucket Problem" are a bucket with a hole in it, an unbroken bucket, and the ability to fill or empty the buckets.

Is there a solution to the "Hole in the Bucket Problem"?

Yes, there are multiple solutions to the "Hole in the Bucket Problem" depending on the specific parameters and constraints given.

What are some real-life applications of the "Hole in the Bucket Problem"?

The "Hole in the Bucket Problem" can be applied in various real-life scenarios such as managing water resources, optimizing production processes, and determining the most efficient way to distribute resources. It can also be used as a teaching tool for problem-solving and critical thinking skills.

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