Momentum (airplane landing, word problem)

[mickeymouseho]

Homework Statement

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?

Homework Equations

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

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!

PS: The answer is 3.4x10^2m according to the answer key.

 

[PhanthomJay]

Newton's laws applied to the boat/plane system don't work very well with relative motion problems when the 2 objects have different accelerations, so look at the plane and boat separately and apply Newton 2 to a FBD of each. What's the net force acting on the plane, and in which direction? What's is the magnitude and direction of the plane's acceleration with respect to the calm sea? What's the net force acting on the boat? What is the acceleration and direction of the boat with respect to the calm sea? What then is the plane's acceleration with respect to the boat? (NOTE: friction force is uN, not um, as you have indicated).