Calculating Maximum Height of a Projectile in Fluid Resistance Problem

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To determine the maximum height of a rock projected upward in water, the force of fluid resistance is modeled as Fd = kv, where k is a constant related to the terminal velocity of 2.0 m/s. The initial speed of the rock is 6.0 m/s, and the buoyancy force can be ignored. To solve the problem, a differential equation must be constructed based on the motion of the rock as it ascends. The first step involves deriving the constant k using the terminal velocity and other relevant constants. This approach will lead to the calculation of the maximum height reached by the rock.
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Homework Statement


A small rock moves in water, and the force (fluid resistance) exerted on it by the water is given by the equation Fd = kv, where k is a constant. The terminal speed of the rock is measured and found to be 2.0m/s. The rock is projected upward at an initial speed of 6.0m/s. You can ignore the buoyancy force on the rock. Find the maximum height that the rock reaches.

I'm not quite sure if there is enough information given to actually solve this question. I can't seem to figure out how to start the question either :(
 
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There's enough information. You have to construct and solve a differential equation for the motion of the rock as it rises. Start by finding an expression for the constant k in terms of the terminal velocity and any other relevant constants.
 
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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