The path r(t)= (t-sin t) i +( 1 - cos t) j describes motion on the cycloid x=t-sin t, y=1- cos t. Find the particle's velocity and acceleration vectors at t equals pi, and sketch them as vectors on the curve.

Certain bacteria (such as aquaspirillum magnetotacticum) tend to swim toward the earth’s geographic north pole because they contain tiny particles, called magnetosomes, that are sensitive to a magnetic field. if a transmission line carrying 100 a is laid underwater, at what range of distances would the magnetic field from this line be great enough to interfere with the migration of these bacteria? (assume that a field less than 5% of the earth’s field would have little effect on the bacteria. take the earth’s field to be 5.0 * 10-5 t, and ignore the effects of the seawater.)