how to determine the initial velocity of the ball when it hits the pendulum and when it hits the floor?

Answer 1

1. Conservation of momentum
I presume that the ball's initial velocity (V0) is the velocity with which it hits the pendulum of mass m2.

m1V0= m1V1 + m2V2
m1(V0-V1)=m2V2

Then

2. V1 will be the horizontal component of the balls velocity after collision.

Vt=V1 + Vy = sqrt( |V1|^2 + |Vy|^2 )

Where Vy= gt

and t= sqrt(2 h / g)

h- height of the point of contact, between the ball and the pendulum, and the floor.
g - acceleration due to gravity.


Just plug the numbers in