How Long Does It Take for Two Rocks Thrown from a Bridge to Hit the Water?

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To determine the time difference between the splashes of two rocks thrown from a 46 m high bridge, one thrown downward at 30 m/s and the other upward at the same speed, the problem requires applying kinematic equations under constant gravitational acceleration. The downward rock's motion can be analyzed using the equation for displacement, while the upward rock's motion involves calculating the time to reach its peak before descending. Ignoring air resistance simplifies the calculations. The key is to find the time it takes for each rock to hit the water and then calculate the difference. Ultimately, the solution reveals the elapsed time between the two splashes.
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Homework Statement



Heather and Jerry are standing on a bridge 46 m above a river. Heather throws a rock straight down with a speed of 30 m/s. Jerry, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance. How much time elapses between the first splash and the second splash?

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The Attempt at a Solution

 
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Solve for the time it takes both rocks to hit the water under a constant gravitational acceleration. You know initial velocity, displacement, and acceleration. All that you need is time. So find the best kinematic equation for your problem.
 
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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