2. (20 points) Two particles move in the x-y plane with positions as functions of time given by
r1(t) = (t^2+2t+2)i + (3t^2-6t+12)j
r2(t) = (4t^2-7t+8)i + (t^2+4t)j
(r, i, j - vectors)
Where t is in seconds and r1 and r2 are in meters.
a. (8 points) At what time do the two particles collide?
b. (12 points) At the moment just before they collide (or at some other time if unable to do part a), determine the velocity of particle 2 relative to particle 1, both of x and y components, and in terms of magnitude and direction.