UCM to Projectile: Optimum Launch Angle/Velocity Dependence?

AI Thread Summary
The discussion centers on the optimal launch angle of a projectile exiting uniform circular motion, which is suggested to vary with initial tangential velocity according to a WinPlot simulation. Participants seek clarification on what constitutes "optimal," defined as the angle that maximizes range. The range equation indicates that, without air drag, a 45-degree angle consistently yields maximum range, irrespective of initial velocity. This raises questions about the simulation's accuracy and the conditions under which the optimal angle is determined. The conversation highlights the need for further exploration of the relationship between launch conditions and projectile motion.
daveschorr
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I ran a simulation on WinPlot (see attached video) on my computer and was a bit surprised to see that the optimal launch angle of a projectile (with NO air drag) leaving uniform circular motion is dependent on the initial tangential velocity (or at least Winplot thinks it does).

Can someone shed some light on this phenomenon or point me to my error?

 
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daveschorr said:
optimal launch angle of a projectile (with NO air drag) leaving uniform circular motion is dependent on the initial tangential velocity
What is "optimal?"
 
By "optimal," I mean the angle that produces the maximum range.
 
daveschorr said:
uniform circular motion
As compared to what sort of launch?
 
Bystander said:
As compared to what sort of launch?
As opposed to being launched from ground level from a cannon or something.
The range equation (with no air drag) is ##R=v^2sin(2a)/(2g)##. In that case the maximum range is achieved by using a 45 degree angle of elevation REGARDLESS of the initial velocity.
 

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