Ken Larsen's web site - Making math relevant

      

If you're a math teacher, here are some problems that can motivate your students to appreciate the value of math:

 

Problem 1:  The fastest space craft that the U.S. has ever made is currently traveling out of our solar system at 10 miles/second.  How long would such a spacecraft take to reach the nearest star?  The nearest star is Proxima Centauri.  It is 4.22 light years away.  Note:  Before your students begin calculating, ask them what their guesses are.  I'll bet they're all extremely low.

 

Problem 2:  Hana is a runner whose personal best in the 5000 meter run is 19:50.  On a 400 meter track, what should Hana's lap times be for Hana to break her personal best?

 

Problem 3:  Hana has heard that running hills is a good way to improve one's sprint speed.  There's a hill near her house.  How can she use Google Earth to calculate its slope?

 

Problem 4:  Bob observes a flash of lightening and hears thunder 15 seconds later.  How far away did the lightening strike?

 

Problem 5:  Ken's dash camera caught this video of a car that was traveling in front of him:   http://kenlarsennc.com/StopSignViolation2016June30Y.mp4

Ken calculated that the car was going 34 miles per hour for the middle section of the video.  How did he figure that out? 

 

To help solve these problems, here are some tips:

Answer to problem 1:  4.22 years * (186282 / 10) = 4.22 * 18,628.2  = 78,611 years

 

However, this assumes that Proxima Centauri remains still ... which it isn't.

 

Answer to problem 2: 

 

19:49 = 19*60 + 49 seconds = 1189 seconds

 

1189 / 12.5 laps = 95.12 seconds per lap

 

Hana's lap times should be:

  1. 1:35

  2. 3:10

  3. 4:45

  4. 6:20

  5. 7:56

  6. 9:31

  7. 11:06

  8. 12:41

  9. 14:16

  10. 15:51

  11. 17:26

  12. 19:01

 

Answer to problem 3:  Google Earth can be used to calculate distances by clicking on Tools, Ruler, and then drawing a line between your starting and ending points.  Specify your distance to be in feet.  Then, hover your cursor over the starting and ending points.  The elevation for each is displayed in the lower right-hand corner of the screen ... "elev 253 ft".  Dividing the elevation change by the distance and multiplying by 100 gives you the percentage slope of the hill.

 

Answer to problem 4:  767 miles/hour X 1 hour/3600 seconds X  15 seconds = 3.2 miles

 

As a rough rule of thumb, it's one mile for each 5 seconds.

 

Answer to problem 5:  Ken noted that the car passed over two sections of dark pavement.  He used Google Earth to calculate the distance between these two dark sections to be 624 feet.  Then, he used a stop watch to time how long it took the car's rear bumper to pass over those sections.  That time was 12.40 seconds. 

 

Speed = distance / time

Speed = (624 feet / 12.40 seconds) * (1 mile / 5280 feet) * (3600 seconds / 1 hour) =  34.31 miles/hour

 

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