Suppose that the position of each of two particles is given by parametric equations. A collision point is a point where the particles are at the same place at the same time. If the particles pass through the same point but at different times, then the paths intersect but the particles don’t collide.

The position of a red particle at time t is given by

x = t + 5    y = t² + 4t + 6

and the position of a blue particle is given by

x = 2t + 1    y = 2t + 6

Their paths are shown in the graph.

(a) Verify that the paths of the particles intersect at the points (1, 6) and (6, 11). Is either of these points a collision point? If so, at what time do the particles collide?

(b) Suppose that the position of a green particle is given by

x = 2t + 4    y = 2t + 9

Show that this particle moves along the same path as the blue particle. Do the red and green particles collide? If so, at what point and at what time?

Transcribed Image Text:

11 6 x