Determining v from momentum / impulse

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Homework Statement
A ball, initially at rest, is struck by a hockey stick. It leaves the hockey stick at speed v. Which quantity, together with the mass of the ball, can be used to determine v?
a) the impulse of the force on the ball
b) the final momentum of the hockey stick
Relevant Equations
momentum, impulse
Answer is (a)

I thought it would be (b) due to conservation of momentum - so final momentum of the hockey stick is equal to the initial momentum of the ball. I assume this isn't correct because there are other external forces acting (air resistance?) Is that sound?
 
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For (b) to be correct, you will also need the initial momentum of the hockey stick. Then the momentum change of the stick will be equal (in magnitude) to the impulse of the force on the ball which brings us to (a).
 
g9WfI said:
final momentum of the hockey stick is equal to the initial momentum of the ball
Further to @kuruman's point, that wouldn't help even if it were true. You know the initial momentum of the ball; you need to find its final momentum.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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