Racing Shells — If you have been to a rowing regatta, you may have observed that the more oarsmen there are in a boat, the faster the boat travels. Investigate whether there is a mathematical relationship between the speed of a boat and the number of crew members.
Consider the following assumptions (partial list) in formulating a model:

a. The total force exerted by the crew is constant for a particular crew throughout the race.

b. The drag force experienced by the boat as it moves through the water is proportional to the square of the velocity times the wet surface area of the hull.

c. Work is defined as force times distance. Power is defined as work per unit time.

When additional oarsmen are added to a shell, it is not obvious whether the amount of force is proportional to the number in the crew or the amount of power is proportional to the number in the crew. Which assumption appears the most reasonable? Which yields a more accurate model?

Transcribed Image Text:

Crew 124 00 8 Distance (m) 2500 2500 2500 2500 Race 1 (sec) 20:53 19:11 16:05 9:19 Race 2 (sec) 22:21 19:17 16:42 9:29 Race 3 (sec) 22:49 20:02 16:43 9:49 Race 4 (sec) 26:52 16:47 9:51 Race 5 (sec) 16:51 10:21 Race 6 (sec) 17:25 10:33