#$&* course Mth 163 Your solution, attempt at solution.
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Given Solution: ** Continue to the next question ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&* ********************************************* Question: `qQuery Introductory Flow Experiment (no summary needed) Is the depth changing at a regular rate, at a faster and faster rate, or at a slower and slower rate? Support your conclusion. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: At a slower and slower rate. As the time goes on, the depth continues to decreas. However, it decreases slower and slower, its starts out decreasing 8.8 cm in 5.3 seconds. Then by the end of the experiment it decreases only 5.4 cm in 5.3 seconds. confidence rating #$&* 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** If you time the water at equal time intervals you should find that the depth changes by less and less with each new interval. If you timed the depth at equal intervals of depth you should find that each interval takes longer than the one before it. Either way you would conclude that water flows from the hole at a decreasing rate. The reason is that as the water depth decreases the pressure forcing the water out of the hole decreases. ** STUDENT COMMENT: I don’t even know how to critique myself on this answer. I did not get it right and did not know how to express how to support my answer (which was wrong). After reading the given solution, I can see what you are looking for in respect to supporting my solutions. I feel that I need to do more to learn how to chart this correctly. This is a topic I will discuss with my tutor. INSTRUCTOR RESPONSE You have stated that you understand the given solution, and given the pattern of the work you have submitted I believe it is likely that you do. In cases where you're not sure you completely understand, it's preferable that you make more specific statements that demonstrate your understanding. I can evaluate and give you feedback on such statements. The key statements in this document are the following: If you timed the depth at equal intervals of depth you should find that each interval takes longer than the one before it. Either way you would conclude that water flows from the hole at a decreasing rate. I don't know whether it's necessary on this problem, but always remember that you are welcome to insert additional statements into a copy of the posted document, mark them with &&&& and submit for further feedback. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique rating #$&*3 ********************************************* Question: `qWhat does the graph of depth vs. clock time look like? Is it increasing or decreasing? Does the rate of increase or decrease speed up or slow down? Does your graph intercept the y axis? Does it intercept the x axis? How would you describe its overall shape? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: My graph starts on the posititve y axis and decreases to the right. confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** The graph will start on the positive y axis and will decrease at a decreasing rate. The shape of the graph is the left-hand side of a parabola that opens upward. The right-hand half of the parabola does not correspond to the flow. The left-hand half of the parabola, which corresponds to the flow, gets less and less steep with increasing clock time, matching the fact that that the rate of decrease is slowing. At the instant the containers empties, the water will be at the level of the hole. If depth is measured relative to the hole, then at the instant depth will reach zero. The corresponding graph point will lie on the t axis and will correspond to the vertex of the parabola. ** STUDENT ANSWER and self-critique: It decreases at a decreasing rate. The graph starts on the y axis, but does not intercept the x axis. It slopes to the right. (self-critique:) I really need to work more on this. This given solution is difficult to follow. INSTRUCTOR COMMENT: Your answer was completely consistent with the first sentence in the given solution, which read 'The graph will start on the positive y axis and will decrease at a decreasing rate'. So you clearly understand that statement, and you gave a good answer to the question. The given solution continues with more details, which you should try to understand and should address in your self-critique. Taking the given solution one statement at a time: The shape of the graph is the left-hand side of a parabola that opens upward. Do you know what a parabola is? This is something you should know from your prerequisite courses, but experience shows that most students have at best a somewhat vague and unspecific understanding of what a parabola is. It's not something that sticks with students from high school courses (and it's not clear that understanding of this term is necessary for passing the SOL, in which case it would not even be taught in most courses). If you don't know, you would ideally state this in your self-critique so I know to clarify it for you. This term will also be clarified in detail in upcoming assignments. For this reason, it's best you should begin to think about it here, and the way to do that would be by asking about it. For reference, a partial picture of a parabola is displayed below: The right-hand half of the parabola does not correspond to the flow. It would be a good idea to have sketched a parabola, opening upward and passing through the positive y axis, according to the given description. With the sketch it's easier to think about why the right-hand side of the parabola doesn't correspond to the flow (for the fairly obvious reason that the right-hand side is increasing and the depth of the water is decreasing; however this would be less obvious without a sketch). The left-hand half of the parabola, which corresponds to the flow, gets less and less steep with increasing clock time ... It would again be useful to have a sketch to refer to. It should be clear that the left- hand side of a parabola which opens upward gets less and less steep as you move to the right. You might or might understand that the vertical coordinate of the graph corresponds to the depth of the water, with depth increasing as you move upward in vertical direction, while the horizontal coordinate corresponds to the clock time, which increases as you move horizontally to the right. ... matching the fact that that the rate of decrease is slowing The rate of decrease is represented by the steepness of the graph. The graph (at least its left-hand half) gets less and less steep as you move to the right. At the instant the containers empties, the water will be at the level of the hole. If depth is measured relative to the hole, then at the instant depth will reach zero. Students often do not understand what it means for the depth to be 'measured relative to the hole'. In this case it would be appropriate to ask about the meaning of this phrase. (The meaning is that the position of the hole would be taken as the 0-point for the measurement, with the upward direction positive so that, for example, a depth of 10 cm means that the water level is 10 cm above the hole). If depth is measured relative to the hole, then since water stops leaking out when the water level is at the hole, the depth would at that point be 0. This would first occur at the instant in time when the depth reaches 0. The corresponding graph point will lie on the t axis and will correspond to the vertex of the parabola. Anyone who does not know what 'the vertex of a parabola' means would certainly be expected to ask. (The vertex of a parabola which opens upward is the lowest point on the parabola. As discussed above this point indicates the depth of the water and the clock time at which the water first reaches the hole. To the right of the vertex, the graph starts rising again and no longer corresponds to the flow situation.) &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):I got the first part right. But I didn't go into enough detail with it. ------------------------------------------------ Self-critique rating #$&*2"