Rowing races have been part of the Summer Olympic Games since 1900, although women's events were not introduced until 1976. While many factors affect the speed which rowers can achieve, we consider the following limited set: . the power P supplied by the rowers (di- mensions of work per unit time); . the submerged volume V of the boat Canadian Teams (which affects buoyancy); . the water density p; . the velocity v of the boat. We also assume that all boats have similar shape (since this affects the drag force). (Continued...) (Continued...) (i) Write down the dimensional matrix, find its rank, and apply the Pi Theorem to show that v = P1/3 p1/3V/2/9. (ii) We see that, since time t o , for a fixed distance, race time t o p3 Vip-3. Assuming that the power Pu exerted by women is about ? the power Pm exerted by men (men are stronger), and also that the submerged volume Vw for women is only about . of the volume Vm for men in a similar boat (women weigh less) what would be the ratio of the race time tw for women to the race time tm for men? (iii) Records indicate that women's race times are about 8% greater than those of men. How does your dimensional analysis prediction compare? How would you explain any differences between the predicted and observed values