Angle at which distance is longest?

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To determine the launch angle for projectile motion when the landing height differs from the launch height, one must consider the vertical displacement in addition to the horizontal distance. The optimal angle for maximum range changes based on the height of the landing position relative to the initial position. For a ball landing on a tower of height h, the angle can be calculated using kinematic equations that incorporate both the initial velocity and the height difference. If aiming for multiple towers, the angle must be adjusted for each specific height to maximize distance. Understanding these principles allows for precise calculations in projectile motion scenarios.
Irrelativity
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I have a question about projectory motion.

I know that if ball is thrown by a person with a initial velocity v(only x and ycomponents), a maximum distance d (distance of x component) can be achived at angle of 45 degree (an angle between the initial velocity and x component of the velocity). But this is only true when the initial position of y component is the same as the terminal position of y conpoment. Here's the my question: how do you guys find the angle at which when the height of a landing position is not the same as the height of the initial position (i.e. Initial y is not equal to terminal y)? Let's say the ball lands on a tower which has a height h with minimum velocity. What's the formula to find the angle?
 
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You mean, what is the angle for the ball to land on the tower? Or to reach maximum range?
Or you have a series of towers and you want to reach the farthest tower possible?
 
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Thread 'Question about pressure of a liquid'

Thread 'Question about pressure of a liquid'

I am looking at pressure in liquids and I am testing my idea. The vertical tube is 100m, the contraption is filled with water. The vertical tube is very thin(maybe 1mm^2 cross section). The area of the base is ~100m^2. Will he top half be launched in the air if suddenly it cracked?- assuming its light enough. I want to test my idea that if I had a thin long ruber tube that I lifted up, then the pressure at "red lines" will be high and that the $force = pressure * area$ would be massive...
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Thread 'Why is the 3 body problem unsolvable? And what will happen if someone solves it?'

I feel it should be solvable we just need to find a perfect pattern, and there will be a general pattern since the forces acting are based on a single function, so..... you can't actually say it is unsolvable right? Cause imaging 3 bodies actually existed somwhere in this universe then nature isn't gonna wait till we predict it! And yea I have checked in many places that tiny changes cause large changes so it becomes chaos........ but still I just can't accept that it is impossible to solve...
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