Suppose that the position of one particle at time is given by x1 3 sin t y1 2 cos t 0 t 2 And the position of a second particle is given by x2 3 cos t y2 1 sin t 0 t 2 (a) Graph the paths of both particles How many points of intersection are there (b) Are any of these points of intersection collisi...

a There are 2 points of intersection 3 0 and approximately 21 14 b A collision poin ...

Suppose that the position of one particle at time is given by x1 = 3 sin t

Question:

Suppose that the position of one particle at time is given by
x1 = 3 sin t y1 = 2 cos t 0 ≤ t ≤ 2π
And the position of a second particle is given by
x2 = -3 + cos t y2 = 1 + sin t 0 ≤ t ≤ 2π
(a) Graph the paths of both particles. How many points of intersection are there?
(b) Are any of these points of intersection collision points? In other words, are the particles ever at the same place at the same time? If so, find the collision points.
(c) Describe what happens if the path of the second particle is given by
x2 = 3 + cos t y2 = 1 + sin t 0 ≤ t ≤ 2π