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 ≤ 2a) 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.