Answer: The spheres exchange velocities after the collision.
Explanation:
If the masses of the spheres are m1 and m2, and we denote their velocities after the collision by x and y, then, according to the law of conservation of momentum,
m1v1 + m2v2 = m1x + m2y. (1)
Using the law of conservation of energy and assuming that the total kinetic energy of the spheres is the same after the collision, we may write
1/2(m1v12) + 1/2(m2v22) = 1/2(m1x2) + 1/2(m2y2) (2)
Solving equations (1) and (2) and setting m1 = m2 = m, we obtain y = v1 and x = v2 , i.e., in a perfectly elastic collision, identical spheres behave as if they exchange their velocities. If, before the collision, the first sphere was moving from left to right with the velocity v1? then after the collision it will move in the opposite direction with the velocity v2.