Question

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

Answer 1

Answer:

there is no collision between the particles

Step-by-step explanation:

for the first particle

x1=3sin t, y1 = 2 cos t, 0 ≤ t ≤ 2π

for the second particle

x2 = -3 + cos t, y2 = 1 + sin t, 0 ≤ t ≤ 2π

then for the collision

x1=x2 → 3*sin t = -3 + cos t → sin t= -1 + (cos t)/3→ 1+ sin t = (1/3)cos t  

y1=y2 → 1 + sin t = 2 cos t → (1/3)cos t  = 2 cos t →(1/3) = 2

since 1/3 ≠ 2 there is no collision between the particles