Suppose that the position of one particle at time t is given...

Suppose that the position of one particle at time $ t $ is given by $$ x_1 = 3 \sin t \quad y_1 = 1 + \sin t \quad 0 \leqslant t \leqslant 2 \pi $$ and the position of a second particle is given by $$ x_2 = 3 + \cos t \quad y_2 = 1 + \sin t \quad 0 \leqslant t \leqslant 2\pi $$ (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 given by $$ x_2 = 3 + \cos t \quad y_2 = 1 + \sin t \quad 0 \leqslant t \leqslant 2\pi $$

Suppose that the position of one particle at time $ t $ is given by
$$ x_1 = 3 \sin t \quad y_1 = 1 + \sin t \quad 0 \leqslant t \leqslant 2 \pi $$
and the position of a second particle is given by
$$ x_2 = 3 + \cos t \quad y_2 = 1 + \sin t \quad 0 \leqslant t \leqslant 2\pi $$
(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 given by
$$ x_2 = 3 + \cos t \quad y_2 = 1 + \sin t \quad 0 \leqslant t \leqslant 2\pi $$

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