Chapter 14.3, Problem 26E

Comparing trajectories Consider the following position functions r and R for two objects.

1. a. Find the interval [c, d] over which the R trajectory is the same as the r trajectory over [a, b].
2. b. Find the velocity for both objects.
3. c. Graph the speed of the two objects over the intervals [a, b] and [c, d], respectively.

24. r(t) = 〈2 cos 2t, $\sqrt{2}\sin 2t,\sqrt{2}\sin 2t$〉, [a, b] = [0, π], R(t) = 〈2 cos 4t, $\sqrt{2}\sin 4t$, $\sqrt{2}\sin 4t$〉 on [c, d]