Adv. function work problem(polynomialf)

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SUMMARY

The problem involves two soccer players running towards each other on an 80-meter field, one at 4 m/s and the other at 5 m/s, for a total of 15 minutes. The key to solving the problem is to calculate the total distance each player covers and determine the instances they pass each other. By plotting their positions over time, one can identify the pattern of passing occurrences, leading to a formula for calculating the total number of passes. The solution involves understanding relative speed and distance covered in a given time frame.

PREREQUISITES
  • Understanding of relative speed calculations
  • Basic knowledge of distance, speed, and time relationships
  • Ability to plot and analyze linear motion
  • Familiarity with polynomial functions for pattern recognition
NEXT STEPS
  • Calculate total distance covered by both runners in 15 minutes
  • Learn how to plot linear motion graphs for multiple objects
  • Explore polynomial functions to derive formulas for motion problems
  • Study relative speed concepts in physics for similar scenarios
USEFUL FOR

Students in physics or mathematics, educators teaching motion problems, and anyone interested in solving real-world applications of relative speed and distance.

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Homework Statement




Two soccer players start at opposite sides of an 80-m field. One runs at 4m/s and the other runs at 5m/s. If they run back and forth for 15 min how many times will they pass each other?


Does anyone know how to solve this?





Homework Equations





The Attempt at a Solution



I tried this one, did 80/4 to get distance ran, then divided that by 900s to get amount of times ran from the track.

900s / 20 laps is 45.

I think that's right, buti don't know where to go from there. What do i do with the second runner? It doesn't work out, any hints, help etc.. please very urgent
 
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If the answer isn't readily apparent, draw a diagram. How many meters will the 4ms runner cover in 15 minutes? How many will the 5ms runner cover?

Now plot the position of the two runners. For example, where are the two runners after 5 seconds? 6 seconds? 7? How about after 10 seconds? Have they passed each other yet? If so, at what time did they pass. Be specific.

Then keep plotting until you discover the second instance of passing. Note the time it occurs. After 3 or 4 passings you'll see the pattern.

Then the formula should become apparent.
 

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