Two particles of equal masses have an elastic collision, the target particle being initially at rest. If it were not a head - on collision, the
directions of their motion after the collision are 

• Our coordinate axes must be one tangential and one along the line connecting the centres of the two objects that will collide. 
• The velocity of the moving ball must now be taken into account because it has two components on the coordinate axis. 
• Assumed in this case is $v_n$based on $v_t$ and normal velocity in the form of tangential velocity.
• The tangential component of a collision cannot alter since there is no impact in that direction. 
• A collision along the normal is comparable to a collision in 1-D. we know that the first particle has no velocity along normal and the second particle will travel along normal.

Hence the correct answer is in mutually perpendicular directions .