I need an advice help with a "Ballistic" problem/task

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The discussion revolves around solving a ballistic problem involving a projectile launched from specific geographic coordinates. The user seeks advice on the correct method to determine the landing point of a mass given its launch angle, speed, and azimuth. There is uncertainty about whether to account for factors like the Coriolis effect or Earth's curvature, although the consensus suggests these may not be necessary for a range of about 1km. Participants emphasize the importance of presenting calculations symbolically and using LaTeX for clarity. Overall, the thread highlights the need for a structured approach to solving the problem while adhering to forum guidelines.
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Hi All,

I am trying to solve the following "puzzle", but I feel like there is information I am missing. Not information in the problem, but a method to solve or something else.

I need your advice or help.


1. Homework Statement


Put a material point with mass 45.93 on the N 42° 38.554 E 023° 13.911 coordinates. Launch it at angle 45° towards horizontal surface, with initial speed 373 km/h, in direction 29,5° azymuth.
With the given details You must find where the ball will fall.

Homework Equations



attached.

The Attempt at a Solution


[/B]
1094m - attached.
 

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  • formula.PNG
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Not sure if you are supposed to consider Coriolis and/or Earth's curvature for the range. Given that it is only about 1km, probably not.
But I should think you are to give the answer as latitude and longitude. You may have to consider curvature for that.

Please do not post working as images. Those are for diagrams and textbook extracts. Take the trouble to type it in.
Also, try to work purely symbolically, only plugging in numbers at the end. There are many advantages, not least that it makes it much easier for others to follow your logic. Rememeber to define your variables.
 
Here's a little brighter version of your image, but haruspex is right -- it's better to type your work into the forum in your future posts here. Thanks.
formula.PNG
 
berkeman said:
it's better to type your work into the forum

And it's even better when you use LaTeX.
 
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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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