How do I get a formula that finds the initial velocity with height in it?

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To find a formula for initial velocity that incorporates height, the discussion centers around deriving the equation from the context of an inclined plane problem involving two steel balls in collision. The equation a(x - x_0) = (1/2)(v^2 - v_0^2) is mentioned, with a request to solve for v_0. Participants highlight the need for additional data, including the angle of the incline and any provided values. Clarification on the problem setup and any attempts made is also encouraged to facilitate the derivation. Understanding these elements is crucial for accurately determining the initial velocity in relation to height.
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How do I get a formula that finds the initial velocity with height in it??

How do I get a formula that finds the initial velocity with height in it??
i was doing a inclined plane problem with is deal with 2 steel balls' collision~
could somebody help me to derivate that formula?
 
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a(x-x_0)=\frac{1}{2}(v^2-v_0^2)

Solve for v_0
 
ya and what is the angle of the inclined place..
 
I am not sure if you had supplied all given data, and of course, your attempt. :P
 
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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