2.2 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,
- What is the best boat's finishing time?
- What is the best boat's average speed?
- At what time is the best boat within 200 meters of the lead boat?
- What handicap would the lead boat receive over the best boat in a 100-km race?
Answers, problem 2
- 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.
- 43/1.852 = 12.537 knots = 23.218 km/hr
- 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.
- (100/43)5 = 11.628 minutes.