Can You Solve the Problem of Projectiles with These Equations?

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The discussion revolves around solving projectile motion problems using specific equations for height and trajectory. Participants emphasize the importance of showing detailed work rather than just stating attempts. Key questions focus on the relationship between the initial speed of one particle and the conditions for tangency with another particle's trajectory. Understanding the starting point and impact point of the particles is crucial for finding solutions. The conversation highlights the need for clarity and thoroughness in problem-solving approaches.
AIshikrakshit
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Homework Statement


upload_2018-3-31_23-56-43.png


Homework Equations


$$h=ut+1/2at^2$$ $$h=x\tan\theta-1/2g\frac{x^2}{u^2\cos^2\theta}$$

The Attempt at a Solution


I tried to take a random angle theta for the lower particee and then using the equation of the upper particle tried to solve them together and find condition for tangency
 

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1) on this forum, "show your work" doesn't mean state that you have done some work, it means SHOW the work
2) what do you know about the point where particle Q hits the ground in terms of the initial speed of particle P?
3) what do you know about the starting point of particle Q in terms of the initial speed of particle 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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