Help with a confusing free-fall motion physics problem?

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The discussion revolves around a physics problem involving two rocks dropped from a building, with one thrown down after a delay. The user is confused about setting up the equations for free-fall motion, particularly regarding the initial velocity and the direction of the vectors. There is uncertainty about whether to consider Lindsay's initial velocity as negative since she throws the rock downward. Additionally, the user questions the correct time variable to use in the equations. Clarification on these points is essential for solving the problem accurately.
Jrohazn
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I'm taking physics for the first time, and I've been attempting the textbook problems, but I can't seem to get it.

1. West stands on the roof of a building, leans over the edge and drops a rock. Lindsay waits 1.25 s after West releases his rock and throws her own rock straight down at 28.0 m/s. Both rocks hit the ground simultaneously. Calculate the common height from which the rocks were released.
2. y=y0+vo(t)-1/2(g)t^2
I'm honestly not even sure how to do it. For Wes: 0=y0-1/2(g)t^2; y0=1/2gt^2
I'm confused on how to set up Lindsay's equation. I checked other people's answers on chegg, and they seem to set up vo as a positive vector, but I thought that since she's throwing down, that it would be negative? Can someone clear that up for me? And for time, would it be (1.25+t)?

Please help :(
 
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I suggest you do not look at other people's answers and try to solve it yourself by thinking instead.

How would you set up the equation that determines how long it takes for Lindsay's rock to hit the ground?
 
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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