# Momentum (airplane landing, word problem)

1. Nov 10, 2008

### mickeymouseho

1. The problem statement, all variables and given/known data

A 1.0 x 10^3 kg plane is trying to make a forced landing on the deck of a 2.0 x 10^3 kg barge at rest on the surface of a calm sea. The only frictional force to consider is between the plane's wheels and the deck; this braking force is constant and is equal to one-quarter of the plane's weight. What must the minimum length of the barge be for the plane to stop safely on deck, if the plane touches down just at the rear end of the deck with a velocity of 5.0 x 10^1 m/s toward the front of the barge?

2. Relevant equations

F = ma
F x delta t = delta p
m1 x delta v1 = - m2 x delta v2

3. The attempt at a solution

I don't know how to approach this problem but this is just a guess.

friction force = 250N (1000x0.25)

force = ma
= 1000kg x 9.8 m/s^2
= 9800N

impulse = mv
= 1000kg x 50m/s
= 50000 kg m/s

delta t = impulse / force
= 50000 / 9800
= 5.1s

mass1 x delta v1 = mass2 x delta v2

1000kg x 50m/s = 2000kg x (delta d / delta t)

[(1000kg x 50m/s) / 2000kg] x delta t = delta d

[(1000kg x 50m/s) / 2000kg] x 5.1s = delta d

127.5m = delta d ?????????????????????

I think this is completely wrong and I don't know what to do with the friction force . Any help would be appreciated. Thanks in advance!