Math 21a, Fall 2008
Problem A, Math 21a, Multivariable Calculus
Rowing problem for Flux integral
Course head: Oliver Knill
Office: SciCtr 434
Problem A:

A Harvard Crew member (who happens to take Math21a this semester) rows on the Charles river. Assume at time t during the drive, her blade is a surface parametrized by
St:  r(u,v) = (x,y,z) = < t+u,u v cos(t), u v sin(t) >,  1 ≤ u ≤ 2,  1 ≤ v ≤ 2
a) Compute the flux of the water force field F(x,y,z) = < -3+z,y,x> through the blade for a fixed time t. This is the power P(t), the rower uses at time t.

b) Integrate the power from t=0, the time the blade is buried, to the time t=Pi/2 when the drive is finished. This is the work, the rower does during one stoke.
Questions and comments to knill@math.harvard.edu