Inelastic collision of plane onto a barge? (challenging)

[lowea001]

Homework Statement

A 1000 kg plane is trying to land on the deck of a 2000 kg barge at rest on the surface of the sea. The only frictional force to consider is between the plane’s wheels and the deck, and this braking force is constant and equal to one-quarter of the plane’s weight. What must the minimum length of the barge be, in order that the plane can stop safely on deck, if the plane touches down just at the rear end of the deck with a velocity of 50 m/s towards the front of the barge?

Note: I don't understand why the initial velocity of the plane relative to the barge cannot be 50 m/s forward, since this value is the initial velocity of the plane relative to the water, and the initial velocity of the barge relative to the water is 0. Shouldn't it make sense that the initial velocity of the plane relative to the barge be 50 m/s? If so, why do the standard equations of motion not yield the correct answer.

P.S. I know you can also solve this question using W=Fd and solve for d, but I want to know how to do it with the relative motion specifically.

Homework Equations

Conservation of linear momentum, F=ma, E=1/2mv^2, W=E2-E1=Fd

The Attempt at a Solution

 

[Dr. Courtney]

Newton's laws apply in an inertial reference frame: the frame of the water, for example.

Since the barge and plane both accelerate, you cannot apply Newton's laws in the frame of the barge.

 

[lowea001]

Newton's laws apply in an inertial reference frame: the frame of the water, for example.

Since the barge and plane both accelerate, you cannot apply Newton's laws in the frame of the barge.

Thank you so much. I was blind but now I see.