Water in Vase Problem

fifthrapiers · #1 $Old$ October 8th, 2009, 01:39 PM

Hi,

I've attached the problem.

I have to determine what's wrong with the student's graph (and what principles the student is understanding).

My thoughts:

It will be the inverse of that graph... that is, there will be a peak initially (since we will have the greatest change in water until we reach the middle), and then we will have extremely little change as there is a lot of volume in the middle, and finally it will peak as the height will increase rapidly.

Any other thoughts?

fifthrapiers · #2 $Old$ October 29th, 2009, 01:29 PM

I asked this question in the beginning of the month and it's still intriguing me. I'm baffled as to what the graph could actually be. Clearly the graph shown is wrong, because then it would imply there is no water, but how would we show a rapid increase followed by a rapid decrease without showing there is no volume?

Soroban · #3 $Old$ October 29th, 2009, 04:34 PM

Hello, fifthrapiers!

Quote:

A vase is one foot tall.
Imagine you are filling the vase with water.
Assuming the water pours at a constant rate,
it takes 10 seconds for the vase to be filled.

Code:

          *     *
         /       \
        /         \
       /:::::::::::\
      *:::::::::::::*
       \:::::::::::/
        \:::::::::/
         \:::::::/
          *-----*

Sketch a graph of the height of the water versus time.

The student provided this response:

Code:

       h|
        |   *
        |  / \
        | /   \
        |/     \
      - + - - - * - - t
        |

According to the student's graph,
the height of the water increases for while
. . then decreases . . . until the vase is empty!

The vase is 12 inches high.
It takes 10 second to fill the vase.

Since the bottom of the vase gets wider,
. . it takes longer to fill the bottom half than the top half.
Let's say, this takes 6 seconds.

The top of the vase gets narrower, so the water level rises faster.
Let's say, the top half takes only 4 seconds to fill.

Then the graph would look something like this:

Code:

        |
     12 +                   o
        |                 * :
        |               *   :
        |             *     :
      6 +           o       :
        |        *  :       :
        |     *     :       :
        |  *        :       :
    - - * - - - - - * - - - * - t
        |           6      10
        |