Answer:
The final velocity is .
Explanation:
Given:
The maximum angle that the pendulum and the ball system can travel, .
The length of the pendulum, .
The mass of the pendulum, .
The mass of the ball, .
Consider that the initial velocity of the ball-pendulum system is . So the initial total energy of the system is given by
Consider the final velocity of the ball is and the final height attended by the system is . So the final total final energy of the system is given by
From the conservation of energy,
From the conservation of momentum,
The final height attended by the system is given by
The final velocity is given by