In which direction does a wall exert the reaction force if it is hit diagonally? I am confused about action-reaction forces and inertia of moving objects. As an example, take a cricket ball a bowler throws to the pitch:

Suppose the ball is about to drop in the pitch with velocity $v$. (the straight black line is the surface of the pitch)
Suppose it drops at $O$ - then it will apply a diagonal force $F_{OA}$ to the surface.
Normally, I think that the surface will react with a force in the $\vec{OC}$ direction - then the ball should move in that direction, but it doesn't, it moves in the $\vec{OB}$ direction.
Why does this happen? Is it because of the ball's inertia?
 A: By the way, OA/OB/OC are not force vectors. The only force vector that is acting on the ball before (and after) it hits the ground is its weight, and it is acting vertically downwards. OA/OB/OC are velocity vectors.
Try to split OA up into its vertical and horizontal components. When the ball hits the floor, reverse the vertical component due to impulse force that accelerates the ball upwards, normal to the surface. The impulse force is much larger in magnitude than its weight, therefore the ball is able to bounce upwards. Now sum up your original horizontal component and the reversed vertical component, you will find that it is equivalent to OB.
A: The force between two colliding bodies is not in the direction of motion. The normal and parallel components have to be treated separately.
The component perpendicular to the contact surface is such that will stop the relative motion and, in case of elastic collision like here, return the system to the same kinetic energy. So ball hitting immovable surface will have the same speed (magnitude of velocity) as before the collision.
There will also be parallel force caused by friction, but it has to be treated separately for two reasons:


*

*The perpendicular force is limited to coefficient of friction times the normal force. If that is not enough to stop the ball, it will skid on the surface.

*The perpendicular force, and this depends on the specific geometry, does not pass through the centre of mass of the ball. Therefore it imparts a moment on the ball that causes it to start rotating. And once the ball is rotating so that the point of contact is stationary, there is no momentum to cause any friction force anymore and the friction force disappears and stops decelerating the ball.


So what happens is that the vertical component of the velocity will be reversed, while the horizontal component will be somewhat reduced with the corresponding amount of kinetic energy transferred to energy of rotation. The rotation will always eliminate the friction force before the horizontal component of velocity is zeroed, so the ball will always continue in the same direction, just a bit slower.
If you instead threw an elastic box (which could not start rotating freely) it could actually bounce back.
A: 
Normally, I think that the surface will react with a force in the OC→ direction 

Yes, if the ball's force on the surface is in direction A, then by Newton's third law, the surface's force on the wall is in direction C. This is what Newton's third law says. The third law applies to all forces in the same way.
However, as pointed out by Jan Hudec in a comment, the ball's force on the surface can't quite be in direction A if the motion is as given. The directions of the two forces should be more like this:

The x components of these forces are frictional. The y components are normal forces.

then the ball should move in that direction, but it doesn't, it moves in the OB→ direction.

Objects don't move in the direction of the force vector. Objects accelerate in the direction of the force vector. In your example, the leftward component of force C decelerates the ball's motion in the x direction, while the y component stops the y motion and then reaccelerates the ball in the positive y direction.
A: As gravity force is their in Y direction so momentum is not conserved but in X direction as MC is valid so no change in the velocity.
if take the components we can see the impulse is in positive Y direction only i.e. direction of force. so acceleration due to collision is in positive Y direction but gravity is their in negative Y direction. in X direction it will continue to move with same velocity. so net velocity vector will be along OB while force is their in only in positive Y direction. 
if fraction is present then it will give a rotational motion to the object. 
