Assignment:
If a metal ball strikes a pendulum and sticks to it. It will have a relationship for conservation of momentum of m*v = (m + M) *V (m and v are the mass and initial velocity of the projectile, M is the mass of the pendulum with no initial velocity and big V is the combined velocity of the pendulum and projectile).
The conservation of energy after the collision is :
1/2 (m + M) * V^2 = (m + M)gh
The vertical rise of the pendulum is represented by h and the horizontal distance swung through is d. The quantities are related by:
R^2 = (R-h)^2 + d^2