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Due on Friday, October 13.
A model for the motion of a moon around a planet is given by the curve
where is the angle .
Plot a picture of the curve between 0 and .
Plot a picture of the speed s(t) against t. From the picture estimate:
Plot the length of the acceleration . From the picture
estimate the magnitudes of the maximal and minimal acceleration between t=0 and .
- The maximum and minimum speed of the particle between t=0 and .
- All times between t=1 and t=2 when the particle will have a speed of 10.
Let be defined by
- Calculate the derivative of f at the point (1,-1).
- Write down the linear approximation g(x,y) to f(x,y)
at the point (1,-1). (So is an affine linear
function whose value and derivative agree with f at (1,-1).
- Now view f and g as vector fields. Use the
Diffeq,Phase Plane program in MacMath to plot a
number of integral curves for each of these vector fields in
the region and .
- Discuss how the two pictures compare.