Why Does the Ball Lag Behind the Falling Board at Angles Less Than 35.3 Degrees?

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The discussion centers on the physics of a ball lagging behind a falling board when elevated at angles less than 35.3 degrees. The problem involves a uniform board of length L, hinged at one end, with a ball positioned at a distance d from the hinge, where d equals Lcos(theta). The calculated free accelerations of the end of the beam and the center of mass are 3/2g and 3/4g, respectively, indicating that the angle of elevation significantly influences the motion of the ball relative to the board.

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problem: a common demonstration, consists of a ball resting at one end of a uniform board of length =L, hinged at the other end, and elevated at an angle theta. a light cup is attached to the board at a distance d from the hinge so that it will catch the ball when the support stick is suddenly removed, which means that d=Lcos(theta) show that the ball will lag behind the falling board when theta is less than 35.3 degrees.

ive found the free acceleration of the end of the beam and the center of mass of the beam which are 3/2g and 3/4g respectively but am not sure where to go from there??
 
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Shouldn't the acceleration at the end of the board depend on the angle of elevation?
 

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