How Fast Does the Water Level Rise in a Triangular Trough?

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Discussion Overview

The discussion revolves around a problem involving the rate at which water level rises in a triangular trough, specifically focusing on the geometry of the trough and the calculations needed to determine the rate of change of the water level given a constant inflow rate. The scope includes mathematical reasoning and problem-solving techniques related to geometry and calculus.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant states the inflow rate and provides a calculated answer for the rate of rise of the water level, suggesting it is 0.77m/min.
  • Another participant requests that the original poster share their attempts at solving the problem to facilitate better assistance.
  • A different participant suggests using the area of the triangle and properties of similar triangles to find the rate of change of the area, proposing a differentiation approach.
  • Another participant questions the initial approach, asserting that the problem involves a triangular prism and provides their own calculations, arriving at a different answer of 0.75m/min.

Areas of Agreement / Disagreement

Participants express differing views on the correct approach to solving the problem, with no consensus reached on the methodology or the final answer. The discussion remains unresolved regarding the best way to calculate the rate of change of the water level.

Contextual Notes

There are unresolved assumptions regarding the application of geometric principles and the differentiation process, as well as potential misinterpretations of the problem's requirements.

decamij
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Water is being pumped into a trough that is 4.5m long and has a cross section in the shape of an equilateral triangle 1.5m on a side. If the rate of inflow is 2m3/min, how fast is the water level rising when the water is 0.5m deep?

Answer is 0.77m/min.

Sorry for not posting this in the homework help section - saw the sign afterwards, and don't really have much time to move it.
 
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Another point is that you should show us what you have already tried- don't just post the problem!
 
Well, I can try to help you, but I don't have enough time to work it out.

You want to find the rate of change of the area, so you'll need to use

a=1/2bh

Then eventually differentiate.

You should use properties of similar triangles to solve for the unknown.

then,
da/dt=(1/2)bh*(db/dt)

and you should be able to know all those variables.

Or else I'm completely wrong
 
But its a triangular prism, isn't it? I don't think just using area will work. I did this:

I use the equilateral triangle to find the height of the prism, and used the equation:

V = 1/2lwh (where l is 4.5, height is 1.5, and width was solved in terms of h).
= 1/2lo.58h^2, (er something like that)
I tried differentiating the equation to get:
dv/dt = 1.16h(dh/dt) --> (i think)


My final answer was 0.75m/min
 

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