Momentum, Impulse, & Collision Homework Questions?

Question

1) The captain of a small barge notices the front corner of the boat is on a collision course with a edge of a small pier. What could he ask the passengers to do to help him avoid a collision?

2) Show that the momentum of a large object is greater than the momentum of a small object even though their kinetic energies are equal.

3) An arrow undergoing projectile motion passes through an apple while travelling at 45 degrees above the horizontal. Can conservation of linear momentum be used to solve this problem?

For #1, I think they have to lean or move a certain way, but I'm not positive. For #2, I'm not sure how to show that. For #3 I just have no clue whatsoever.

Could you please explain, rather than just giving me the answer? I'd really appreciate it.

Thanks in advance. :)

Answer 1

1)  They need to move toward the side of the boat where the collision is likely.  This will cause the boat to move in the opposite direction even though the CM of the combined boat + people continues on the same path.

2)  Let M = k*m where k > 1.0  Then mv² = kmV² for the KE's to be equal.  Solving for V, V = v/√k.  Ergo,

MV = km*v/√k = √k*mv.    Since k>1, MV will be >mv

3)  You have not posed a problem to solve; only described an initial condition.