Abstract: Traffic control is necessary for traffic safety in driving cars. To avoid collision of cars in crossroads is an important practical problem. We study in this paper the collision problem of two cars in elliptical forms which move with uniform speed on two crossroads orthogonal to each other. In applying Wu Wen-tsun's method of mathematics-mechanization we find conditions such that collision will not occur. We have also determined in the possible colliding case the time and place of first collision.

Key words: Mathematics-Mechanization, Wu's method, Collision problem, Characteristic set