Topics
2. Linear Relations and Equations
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AustraliaVIC
VCE 11 General 2023

INVESTIGATION: Filling a pool

Lesson
Lesson
Overview
Activity
Reflection

Investigate the process of filling a swimming pool by examining the flow of water from a sink into a measuring cup.

Objectives
  • To practice differentiating between functions and relations.
  • To practice identifying linear relationships in real-life.
  • To practice using the two point formula.
Materials
  • Clear measuring cup (holds at least 4 cups)
  • Marker
  • Sink
  • Stopwatch
  • Paper
  • Internet

Filling a Swimming Pool

Procedure
  • Place the measuring cup into the sink.
  • Turn on the sink and begin the stopwatch at the same time.
  • Every 5 seconds turn off the sink and record how much water is in the measuring cup.
  • Use this table to record your data:
  • Stop when the measuring cup is filled.
Investigate
1.
Pick two data points from what you collected and use the two points to determine the rate of change of volume per second or the gradient.
2.
Choose two more pairs of points and repeat the process. Are the three gradients different? Comment.
3.
Determine the rate of change of volume per second using the average of three gradients you have found.
4.
What is the independent variable and dependent variable?
5.
Construct a linear function to represent the situation.
6.
Graph the linear function, clearly labelling each axis. Which axis does the independent variable go on? Which axis does the dependent variable go on?
7.
What is the y-intercept of your graph? Explain why this makes sense in the context of the experiment.
8.
Would the graph look the same if you had begun the experiment with some water already in the measuring cup? If not, how would it have changed?

Work with a partner to answer the remaining questions.

Discussion
1.
Compare your graphs. Did your measuring cup fill up faster than theirs? Why or why not?
2.
DDetermine how long it would take to fill up a swimming pool assuming the water was pumped into the pool at the same rate the sink was pumping out water. You may need to use the internet to find additional information.
3.
How long will it take for the pool to overflow?
4.
Is this a reasonable rate at which to fill up a pool? Why or why not?

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