How does the release angle of a catapult affect the object's velocity?

[Generally Confused]

TL;DR Summary

HELP - THIS IS URGENT!!!
I'm trying to determine the relationship between a catapult's release angle and the average velocity of the projectile, but I'm having trouble finding an equation that could be derived for this purpose. I'd really appreciate any help you can give! :)

NOTE: Even if you just help me out with the equation and leave me to understand it on my own, that's okay. I just need to somehow get to an equation.

[Moderator: repeated text removed.]

 

[rexxii]

https://keisan.casio.com/exec/system/1225094602
dont know if this helps or not?

 

[sophiecentaur]

https://keisan.casio.com/exec/system/1225094602
dont know if this helps or not?

It's possible that the OP is confusing velocity with actual range? That link would be what's needed if that's the case.

 

[phinds]

I'm trying to determine the relationship between a catapult's release angle and the average velocity of the projectile

Are you sure that's really what you want? The average velocity? That seems like a useless figure to me. Even if you are looking for the RELEASE velocity, that's also pretty useless. What's normally wanted in a catpult is to optimize the range.

 

[sophiecentaur]

What's normally wanted in a catpult is to optimize the range.

Not necessarily. It is often required to have the stone traveling at a 'useful' speed when it hits the target. For ranges below the maximum there are two elevation options (ideal parabolic trajectory) for a given initial speed. But the Maths of this is so well known (see the link mentioned higher up the thread) that attempts at simple verbal descriptions tend to be counter productive.