Final answer:
In an elastic collision where two particles have the same mass and one is initially at rest, they will move in mutually perpendicular directions after the collision, due to the conservation of both momentum and kinetic energy.
Step-by-step explanation:
The question relates to elastic collisions in one-dimensional motion where two particles, A and B, have the same mass, and B is initially at rest. In an elastic collision, both momentum and kinetic energy are conserved. When two objects of the same mass collide elastically, and one is at rest, they will exchange velocities if they move along the same line. The correct answer in a case where they collide at an angle is that they will move in mutually perpendicular directions after the collision, assuming an ideal two-dimensional elastic collision with equal masses and one is initially at rest. This is because the angles in such a collision are related to the conservation of momentum and the need to keep the total kinetic energy constant.
Here is an example related to the question: In an elastic collision between two objects of equal mass where object A is initially moving with a known velocity and object B is at rest, after the collision, A comes to rest and B starts moving with the initial velocity of A. This example is for one-dimensional motion along a straight line and the velocities are exchanged, which differs slightly from the original question that considers an oblique collision.