A ball collides with a vertical, unmovable wall. There is no friction between the wall and the ball (the only force acting on th

Answer: in the same direction, meaning to the left.

Explanation:

The force acting perpendicularly to the surface in contact is such that it halts relative motion and, in the case of an elastic collision like this, restores the system's kinetic energy to its previous level. Thus, when a ball strikes an immovable surface, its speed (velocity magnitude) remains unchanged following the impact.

There will be a frictional force acting in parallel, but this should be examined separately for two main reasons:

The perpendicular force is constrained to the product of the coefficient of friction and the normal force. If this is insufficient to halt the ball, skidding will occur. The perpendicular force, which relies on the specific shape involved, does not align with the ball's center of mass, producing a torque that induces rotation. Once the ball rotates in such a way that the contact point is stationary, the momentum that would otherwise create friction force vanishes, causing the friction to cease, thus halting the ball's deceleration.

Consequently, the vertical component of the velocity will be inverted, whereas the horizontal component will be reduced to some extent, transferring a portion of kinetic energy into rotational energy. The rotation process will always negate the friction force before the horizontal velocity reaches zero, allowing the ball to keep moving in the same direction, albeit at a slower pace.

If instead you were to throw an elastic box (which wouldn't be able to rotate freely), it could indeed bounce back.