Find launch angle given height, velocity, and vertex

[gum444]

1. What do you want to achieve? I want to calculate the launch angle given the initial height (0,-1), velocity (3000), gravity (196.2) and vertex (100,0).

2. What is the issue? I don’t know if this is the right place to ask but I figured a lot of people here are good at math so maybe someone could help.

3. What solutions have you tried so far? I’ve searched the internet and used ChatGPT to try and find an answer but I couldn’t find one. I’m not good at math so maybe I don’t know what to search for.

Sorry if this post seems lazy. I’ve been trying to figure out how to accomplish this all day but to no avail have I found an answer. What I’m trying to do is create an equation that takes into consideration zeroing, where the projectile will hit center at X meters, or in my case at the vertex (100,0). Is it possible to find the launch angle given only height, velocity, gravity and vertex?

Apologies if this was the wrong forum to ask.

[Emskipo]

What you’re looking to find is Trajectory formula/equation. The 2D Trajectory formula should be sufficient. You can google this and find all sorts of tutorials explaining it. I personally like Kahn Academy; they have great video lessons on mathematics.

[gum444]

Thanks for the recommendation. I currently have a ballistics system in place that moves a bullet along a trajectory given a velocity and direction. I’m just trying to incorporate zeroing of 100 studs into the direction the bullet is traveling.

I know how to calculate the angle based on range, but what I actually want to do is have the bullet hit the target at the parabola’s vertex. I’m noticing that the vertex occurs at about half the range of the trajectory, but I also need to consider the height (-1 below the camera) and the landing position which should be the vertex (same y-value as camera, or 0)

[gum444]

Graph

This is how I calculated where the projectile should land, but what I’m trying to do is move the vertex to the x-intercept (100,0)

[Emskipo]

The maximum height of the trajectory is exactly what you want. If you study the formula you can solve for the values required to ensure that the max height is at the value you require.

[Prototrode (小蜜梨)]

Why would you ever need to solve for launch angle using only a polynomial in vertex form, in a 3D video game engine? You should only need the vector positions and velocities.

Here’s a guide that might be helpful:

Modeling a projectile's motion

This guide was originally written for scriptinghelpers. The original can be found here. As a somewhat active member of the Scripting Helpers discord one of the most common questions I see is how to have a projectile travel an arc. Most people want to know how to do this for things like basketballs or cannon balls and so forth. Since this is such a popular question I thought it would be worth writing a blog post on it and talking about a few other things we can extend from our findings. Deri…

And here’s my take on a ballistic solver that uses a quartic equation:

Predict projectile ballistics, including gravity and motion

I don’t think anyone here would want to learn how it works, and I don’t blame you. I plagiarized all of this from the internet and somehow botched it into a working package so that you don’t have to. What is this? An actual, accurate projectile ballistic trajectory calculator. If you’ve ever played WarThunder, you should be familiar with this (the little reticle that leads ahead of an enemy craft? That’s exactly what this is.) [image] What can this be used for? If you’re designing a war-the…

[gum444]

After doing some research I realized this system isn’t actually what I need, but thanks for pointing me in the right direction