Does the movement of a passenger change the velocity of an aeroplane? I encountered a problem in my physics textbook today.

An aeroplane of total mass of 50,000kg is travelling at a speed of 200m/s. If a passenger of mass 100kg then walks toward the front of the aeroplane at a speed of 2m/s, what change in the speed of the aeroplane does this cause?

It's easy enough to solve with the law of conservation of linear momentum. But my question is why? How?
Because as you move forward in the plane, there is no external force on the system. So it shouldn't effect the plane.
p.s- I'm new to this concept and would be grateful for an in depth walkthrough.
Edit:- The answer in the book says that it's supposed to be 4mm/s difference in velocity. No direction stated. Also, by looking at all of the answers you have given me, I think it's safe to say that there is no 'true' answer. Both interpretations are equally correct
 A: What would happen if instead you imagine the plane to be no longer in air, but instead it is floating on a large, still bed of water? I use this example so as to have a situation where there is no friction. Now if you are inside the plane and then run forward will the plane begin to move backward?
The answer is obviously no. You are correct in that Newton’s second law applies to external forces. A man inside the plane has no way to exert an external force on the plane.
This particular example considers possible action reaction pairs. Newton’s third law of motion states that “If an object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A“. But here, object A is the mans feet and object B would be the floor of the plane. If the floor then exerts a force on say the planes chassis, that chassis will then push back on the floor etc. so that there is never a resultant force on the plane itself. Of course this would be different if the man got out and ran along the outside (top) roof of the plane.
You asked about conservation of momentum? The law of conservation of momentum can be stated the total momentum of a system remains constant if the net external force acting on that system remains zero
And importantly:
The total momentum of a system is defined as the vector sum of the momenta of all the objects in that system. According to the law of conservation of momentum, the total momentum of a system remains constant as long as the net external force on that system is zero. The forces present between the objects inside the system are called internal forces. These internal forces do not change the total momentum of a system.
I guess the question that was asked was worded in such a way as to confuse, but the data in that question are red herrings.
A: Well here's the thing : If you consider the aeroplane as a separate body its velocity would change because friction applied by you on the plane would then be considered as an external force but if you consider yourself and the plane as a system then the net velocity of the centre of mass of the " you and plane" system would not change since the friction force applied by you on the plane would now be considered as an internal force .
A: You have three main systems in your question - the plane, the passenger and the plane+passenger.
The plane + passenger system can be considered isolated in the example, no external force is acting on it, so its center of mass remains at constant velocity.
The plane itself has an external force acting on it by passengers feet when he/she tries to change his/her state of motion form rest (relative to the plane) to walk, thus the plane will move in the opposite direction to the passenger.
The passenger has an external force acting on him/her by the reaction of the plane and this enables him/her to start walking.
Due to the third Newton law, motions of the plane and the passenger systems are "opposite to each other" and cancel each other out, so that the center of mass of the plane+passenger system will not change its motion.
Perhaps a little confusing might be, that the passenger is geometrically inside the plane, so the name "external" has wrong visual connotation. But when we talk about systems we distinguish internal/external force based on whether it was produced by objects that are considered to be part of the system versus forces between objects in the system and objects that are not considered part of the system and not by geometrical relations.
A: I'm pretty confident that the problem means for us to consider the plane as a system not including the passenger. In this case, as other answers have pointed out, the passenger is 'external' to the plane system, and therefore any force the passenger exerts on the plane is an external force on the plane system.
Now for the nuts and bolts of the force interactions.
Ignoring several unnecessary complications (e.g. air drag on the passenger), the passenger is acted upon by three forces -- gravity pushing him into the floor of the plane, the normal force from the plane reacting to that gravity, and the static friction between the passenger's feet and the plane floor that actually propels the passenger forward to his/her 2 m/s walk speed. Two of these forces -- the normal force and the friction force -- come from interactions with the plane, and so, by Newton's third law, there are corresponding forces acting on the plane.
The plane, meanwhile, is acted upon by gravity, by lift, and by the reaction forces to the normal and friction forces on the person (ignoring, e.g, drag and thrust). Under the assumption that the airplane maintains level flight, the gravity and normal forces will cancel with lift, and in any event these forces aren't changed by the passenger's acceleration. That leaves the reaction to the friction force, accelerating the airplane backward in response to the person's forward acceleration.

Thus, as the passenger accelerates forward, the plane accelerates backward, and by the time the passenger has reached his 2 m/s walk, the plane's velocity will have changed accordingly.
By analogy, think about what would happen if you hopped forward off a stationary skateboard. It should come as no surprise that the skateboard would be propelled backward in response.
Now let's briefly look at this in terms of the system containing both plane and passenger. In this system, indeed, there is no net external force, and so the center of mass of the system undergoes no change in velocity. However, the mass distribution of the system does change; the person accelerates forward, and so the plane must accelerate backward to maintain the center of mass.
Of course, eventually our passenger will walk headlong into the closed and locked door to the cockpit, at which point this will all happen in reverse and the plane will return to its original velocity, while the passenger is directed sternly back to his/her seat.
(As a side note, we are ignoring the competing drag and thrust on the plane that maintain its velocity. On a real plane, passengers moving back and forth just form small perturbations around an equilibrium velocity, the effects of which are quickly damped out.)
A: Approach 1:
Consider the plane and the man as a single system. Since there are no external forces acting on them, the center of mass shouldn't accelerate. But if the man starts running to the right and the plane doesn't react to this, the center of mass would go to the right as well. So in order for the center of mass to stay where it is the plane that should accelerate in the opposite direction.
Approach 2:
When you start walking on a plane your feet "rubs" against the floor of the plane, thus pushes it in the opposite direction that you are moving in. As you gain speed in one direction, the plane does in the other.
But here's the thing: When you're trying to stop the reverse happens and as you come to a stop, the plane goes back to its original speed.
A little more elaboration
Someone asked for a mathemetical proof for the first approach. So first check out the attached photo.

As you see their accelerations are opposite. Furthermore note that ap*mp = -am*mm. Left side of the equation is the total force on the plane, whereas the right side is that on the man times -1. These two forces make up an action-reaction pair. Since it is the man pushing against the floor of the plane it makes sense for the plane to push the man back with an equal but opposite force.
So we have also derived Newton’s third law using his second law. By which I mean the man+plane system has no external forces on it, so we asserted that the center of mass doesn’t accelerate.
Another outcome of this result can be understood by realising that the mass of the plane is so much larger than the man such that the ratio mm/mp is almost zero. Thus, even though the plane slows down due to the acceleration of the man, the decrease in its velocity is not large enough to be noticable.
