MS 095 PreAlgebra Worksheet	Name: ____________________

Trackulations

The following problems are based on data gathered while jogging and juggling at the Pohnpei state track on 26 March 2005. Twenty-two laps were run, primarily in lane four, while various other parameters were measured either electronically or by manual counts.

Terminology:

Lap time: the time to complete one lap.

Distance: the distance for one lap, varies with the lane.

Heart rate: the number of heart beats per minute (a unit rate).

Cadence: the number of right foot falls per minute (a unit rate).

Cycle: a cycle is tossing each of the three tennis balls once.

Tosses: The total number of tennis ball throws by one hand. Tosses is cycles multiplied by three.

1. Divide the distance for one lap, 435 meters, by 1000 to obtain the distance in kilometers.

435 ÷ 1000 = _______________ kilometers

2. Convert the distance in kilometers to miles: ________________

3. Convert the distance in meters to feet: ________________

4. Divide the time for one lap, minutes, by the distance for one lap in kilometers to obtain my pace in minutes per kilometer.

= _______________ pace in minutes per kilometer.

5. Muliply the lap time of by 60 to get the lap time in seconds. Keep track of this number, you will use it later.

= _______________ lap time in seconds.

6. Divide the distance of one lap in meters by the lap time in seconds to get my speed in meters per second:

= _______________ speed in meters per second.

7. Go back to the golf ball laboratory. How far would a golf ball have to fall to reach this speed?

8. During a single lap I counted 69.5 cycles. Multiply by three to get the total tosses in a single lap:

69.5 × 3 = ____________ tosses for single lap

9. Divide the total tosses for a single lap by the lap time in seconds to determine the tosses per second: ___________________

10. Divide the total tosses for a single lap by 435 to determine the tosses per meter: ______________

11. Calculate the inverse of the tosses per meter to determine the distance I cover of the track between tosses of the balls:

= ________________ meters covered between tosses

12. Multiply the heart rate of 158 heart beats per minute by the time for one lap of minutes to get the number of heart beats per lap:

= ________________ heart beats per lap

13. Divide the total tosses for a single lap by the heart beats per lap to determine the tosses per heart beat: ________________________ tosses per heart beat

14. Calculate the inverse of the tosses per heart beat to determine the number of heart beats per toss:

= ___________________ heart beats per toss

15. During a single lap I make 206 right foot falls. Calculate the number of right foot falls for a typical set of twelve laps: ____________________

16. Divide to determine the right foot falls per minute (cadence): __________ cadence

17. The ideal cadence for a runner is 85 to 90 per minute. Is my cadence (my leg turn-over) too slow or too fast?

18. Divide the tosses per lap by the 206 right foot falls per lap to determine the tosses per foot fall: ____________________ tosses per right foot fall.

19. Calculate the inverse of the tosses per foot fall: ____________________ right foot falls per toss.

20. Divide 206 right foot falls per lap by 435 meters to determine the foot falls per meter.

______________ foot falls per meter

21. Divide 435 meters by 206 right foot falls per lap to determine the distance I cover between right foot falls: __________________

22. Express rounded to the nearest whole number ratio the following ratio series:

heart beats per toss : right foot falls per toss: tosses per toss (1)

Use the values calculated above for these quantities to complete the triple ratio below.

_______________ : ______________ : 1

23. If your calculations are correct, my cadence is not optimal. The above ratio, if correctly calculated shows that there is a linkage between tosses and cadence. There is a synchronization between ones legs and juggling tosses when running and juggling. A juggling ball, however, obeys the laws of gravity. The time aloft for a ball depends strictly on the height of the throw. Divide minutes by 69.5 cycles per lap and then multiply by 60 to determine the seconds per cycle:

= _____________________ seconds per cycle.

24. During a cycle any one given ball makes a two arcs, one to the left, one back to the right. That makes two rises and two falls. The time for a single fall is thus one quarter of the seconds per cycle. Multiply the seconds per cycle by to obtain the time for a ball to fall. __________________ ball fall time

25. The distance for a single fall is given by the equation:

where g is the acceleration of gravity 10 m/s² and t is the ball fall time. Calculate the distance d the ball falls: _______________________ distance.

26. Toughie: To bring my cadence closer to optimal, would I have to throw the balls higher or lower? __________________________

Dana Lee Ling

2005-04-03T09:37:52