Minimum Length for Safe 1000kg Plane Landing on 2000kg Barge

[sean-820]

Homework Statement

1000kg plane lands on a 2000kg barge on in a calm ocean. The only frictional force is equal to one quarter of the planes weight. What must the minimum barge length be to land safely if it hits the deck at 50m/s. Also there is no water friction/resistance.

Homework Equations

mv=mv1+ mv2 (conservation of momentum)

FT=m (v2-v1) (impulse=change in momentum)

distance=VT

The Attempt at a Solution

I think i may have the right answer now, but I am not totally sure.

The momentum of the plane = 1000x50=50000
With twice the planes mass, the 50m/s plane will transfer all of its momentum to pushing the barge back at 25m/s.

Using friction=0.25mg the frictional force =250x9.8=2450N

T=(m(v2-v1))/F
=(1000(-50))/-24500
=20.4seconds

Then using D=VT=25 (20.4) i found the distance traveled must be at least 510m.

What I'm asking does this seem logical and correct? i think it may be, but I'm not totally sure. I wasn't provided the correct answer




Also, is there some way you can go back and read all your own posts?

 

[sean-820]

The main thing that I'm not sure on is the impulse = change in momentum. For the mass would i have to do m1 or the total m1+m1 mass?