1) In the initial situation, the total mechanical energy of the system is given only by the kinetic energy of the ball that is moving with speed v:
where
is the mass of the ball.
In the final situation, where the system (ball+pendulum) rises a vertical distance of h=0.145 m, the system is stationary (v=0) so the total mechanical energy of the system is the gravitational potential energy:
where
is the mass of the pendulum.
For the law of conservation of energy,
, so we can find the initial speed v of the ball:
2) The kinetic energy lost in the collision is the initial kinetic energy of the ball: