Deriving the Angle of Release for a Simple Pendulum: Help Needed!

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To derive the angle of release for a simple pendulum, the user has determined the height using the formula mgh=(mv^2)/2, based on known mass and velocity at the lowest point. However, they are struggling with the geometric and trigonometric aspects needed to calculate the angle, particularly without knowing the length of the string. A response suggests that without the string length, finding the angle of release may not be feasible. The discussion highlights the importance of string length in pendulum calculations. Overall, the user seeks guidance on how to proceed with their calculations.
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I have looked through the forum here and several other forces. My task is to derive a formula to determine the angle of release of a simple pendulum. I know the mass, velocity at lowest point and I can therefore determine the height or distance it fell mgh=(mv^2)/2. I am not able to locate the geometric/trig brain cells that will let me use this information to determine the angle athough I do know the adjacent side of the similar but smaller triangle. I do not know the length of the string. Could someone point me in the right direction please?
 
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If you don't know the length of the string, I don't see how you can find the angle of release.
 
uh-oh, that does not sound promising. Thanks anyway.
 

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