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 22.224 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?

Answers, problem 2

  1. The lead boat finishes in 43/22.224 = 1.935 hours, or 1 hour and 56.1 minutes. The best boat started 5 minutes behind, so has a time of 1 hour 51.1 minutes = 1.852 hours.
  2. 43/1.852 = 12.537 knots = 23.218 km/hr
  3. A 5-minute head start gives the lead boat a distance of 1852 meters in front of the fast boat. This is made up exactly over the entire race. Assuming constant speeds for both boats, the race will be (1852 – 1652)/1852 = 89.2% finished when the fast boat closes to within 200 meters. This happens at time 1.652 hours = 1 hour 39.12 minutes.
  4. (100/43)5 = 11.628 minutes.

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