Last revised 1997/09/22 |
91. Be careful to keep track of what is measured by what observer.
V. Make sure you draw a diagram. The man can, of course, head partly up- or down-stream while he is rowing. How do you find the minimum of a function?
You might want to review the solution of problem IV.
VI. There are two different kinds of problems hidden here. What are they, and what kind of physical problem is each one? How do you handle the effects of tangential acceleration?
VII. What is the magnitude of r as a function of time?
Math notes
d f(at)/dt = a df/dt, special case of chain rule d f( g(t) )/dt = (df/dg)(dg/dt)
d cos(wt)/dt = -w sin(wt)
d sin(wt)/dt = w cos(wt)
d (xy)/dt = dx/dt y + x dy/dt
A vector written in terms of unchanging unit vectors may be differentiated using the product rule and
di / dt = 0 (etc.)
Hence if
v = vy j
then
dv / dt = ( dvy/dt ) j
You might also find it useful to use
d w2 /dt = 2 w dw/dt
in seeking places where dw/dt vanishes, especially if w involves a square root.
10. No hint, except to remember that forces are vectors.
11. (a) and (b) are pretty easy. In (c), you should be able to achieve a = 0.