Question

In rowing, the split time is the time it takes to row a distance of 500 m. There are formulas that estimate the total work done by a row in a certain amount of time; the formulas are proportional to 1/T^3, where T is the split time. Explain why thus us true.

Answer 1

Unlike the motion on land, the motion on water has a much higher resistance from the medium. The drag due to air resistance can be neglected on land.

But on water, the drag can not be neglected.

The drag on water due to the friction between the water and the boat is called skin drag.

The skin drag is proportional to the square of velocity

R = av²

A force equal to maintain the body in a constant velocity is equal to the drag force.

So, power required = Force* Velocity

P = av³

Since split time is the time taken to row a distance of 500 m,

velocity is equal to

v = 500/T

So,

P = a*(500/T)³ = k/T³

So, the total work done to row a certain amount of time is

W = P*t = kt/T³

So, work done is proportional to 1/T³