Parabolic Motion of a projectile

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To analyze the parabolic motion of a projectile, key equations include R = (vi^2 * sin(2θi)) / g for range and h = (vi^2 * sin^2(θi)) / (2g) for maximum height. The goal is to determine initial velocity (vi) and direction (θi) based on user inputs for maximum height and distance covered. The discussion emphasizes the need to rearrange these equations to solve for vi and θi. Understanding these relationships is crucial for accurately modeling projectile motion.
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Homework Statement

I'm trying to find a equation that will connect a object that is thrown to form a parabolic motion of a projectile. What I want to be able to sub it in is maxheight and displacement covered by the projectile


Homework Equations



I don't really know, maybe vi = vf + a*t?



The Attempt at a Solution



Went to google equations of it and some other sites, I won't list them all here because I searched almost all the sites.

http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Vectors/ProjectilesMotion.html
 
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So you want to be able to say simply it's maximum height and its distance covered and find out its initial velocity and direction? Or the other way around?
 
The maximum height and distance user inputted. Find initial velocity. Direction is calculated already.
 
Do you mean using R={v_i^2\sin2\theta_i\over g} and h={v_i^2\sin^2\theta_i\over 2g} to get v_i ?
 
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