The Legacy of Newton, Gallileo, and Leibniz: Quiz


Problem 2

In a handicapped sporting contest, such as sailing, a competitor with a better previous winning record receives a shorter head start than a competitor with a worse record. In an ideal race, all the boats would cross the finish line at exactly the same time.

Suppose that in a 43-km sailing race the first boat out has a 5-minute head start on the best boat. The average speed of the first boat is 12 knots, or 22.22 kilometers per hour.

Assuming both boats travel at a constant speed in an ideal race,

  1. What is the best boat's finishing time?
  2. What is the best boat's average speed?
  3. At what time is the best boat within 200 meters of the lead boat?
  4. What handicap would the lead boat receive over the best boat in a 100-km race?

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