Transverse wave through a medium

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In a transverse wave, the medium moves perpendicular to the direction of wave propagation. At point P, the instantaneous velocity of the medium is vertical, meaning it can only move up or down. As the wave travels to the right, point P will soon reach the peak of the wave, indicating that its velocity is upwards at that moment. The initial reasoning that the medium moves downwards is incorrect, as it will be moving upwards when it reaches the peak. Understanding the relationship between wave direction and medium movement clarifies the instantaneous velocity at point P.
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Here's the question:

The transverse wave shown is traveling from left to right in a medium. The direction of the instantaneous velocity of the medium at point P is:

f17020.jpg


A. no direction since v = 0
B. to the right
C. upwards
D. at an angle upwards and to the right
E. downwards


Here's my (most likely wrong) reasoning. It's a transverse wave so the medium either moves up or down. I'd say at point P the medium is moving downwards because after point P the medium is below the axis? Can someone please explain what I'm not getting here? Thanks
 
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As the wave is moving to the right, then the peak you see in the wave which is to the left of P, is moving towards P. Very shortly, P will be at the top of that peak. (The point P cannot move to the left or right itself, only up or down)
 
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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