Cambridge O Level Additional Mathematics · Syllabus 4037 · Vectors in Two Dimensions
Collision Condition
What is Collision Condition?
The requirement that two moving particles occupy the same position at the same instant. For particles with constant velocities, positions are written as r equals r nought plus t v, and the test is to set the two position vectors equal, giving one equation from the x components and one from the y components. Both equations must yield the same value of t for a collision to occur, and that value must be physically admissible, normally t greater than or equal to zero. If the two equations give different times, the paths may still intersect geometrically but the particles pass through the crossing point at different moments and do not meet. The collision position is found by substituting the common time into either particle's position vector, and confirming it with the other.
This definition is part of the Vectors in Two Dimensions chapter in Cambridge O Level Additional Mathematics.