1 / 18

Advance Proportions

Learn how to solve for k in advanced proportions and graph relationships using natural and linearized graphs. Apply these skills to real-world scenarios such as determining the time it takes for a rock to fall from a given height.

alfonsom
Download Presentation

Advance Proportions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Advance Proportions Unit 1 - Science

  2. Advanced Proportions • If Y2 is directly proportional to X then… …If X doubles, Y will __________________. Square root two

  3. Equations: Y2 = k X Or Y =√kX

  4. How do I solve for K? • Graph Y2 vs. X & the slope = k

  5. Natural Graph vs. Linearized Graph • NATURAL GRAPH: • LINEARIZED GRAPH: Y2 Y X X

  6. Example: • You are curious if there is a relationship between the height of a cliff and the time it takes a rock to fall to the bottom. You drop several rocks off of several cliffs and record the following data…

  7. Here is the data you collect:

  8. Graph the information on the first graph grid in your notes.

  9. Your graph should look similar to this: Cliff Height and Drop Time Time (s) Height (m)

  10. Now we need to linearize the graph: • To do this we will graph Y2 and X. • First we need to change our data table.

  11. Our new data table will look like this:

  12. Graph the information on the second graph grid in your notes.

  13. Your graph should look similar to this: Y2 X

  14. Next Steps: • Write the EQUATION FORM: Y2 = kX • Circle your cross points. • Cross Points = (0,0) & (100, 20) • Solve for K. • K = (20-0)/(100-0) = 20/100 = 0.2

  15. So our real world equation is: t2 = 0.2 h Where t is the time & h is the height of the cliff.

  16. Summing it up! • Based on the shape of your graph, the time squared is directlyproportional to cliff height. • This means if if a cliff is THREE times taller it will take the square root of three times longer to reach the bottom! • Use your real world equation to predict how much time it will take if you drop a rock from a 300 m cliff. Answer: 7.75 seconds

  17. Now try it on your own! Go back to your Lagoon graph from the basic graphs lab and determine the real world equation.

  18. Now let’s do a real world application. Follow the instructions for the Impact Lab found below.

More Related