In order for there to be a collision the initial velocity of the
club head must be greater than the initial velocity of the golf ball.
Also for there to be separation, the final velocity of the golf ball
must be greater than the final velocity of the club head. Thus the
equation for elasticity (e) of the golf ball.
1) e = (vf - Vf) / (Vi
where V is the velocity of the club head, and v is the velocity of
the golf ball.
Using the principle of conservation of momentum:
2) MVi + mvi = MVf
where M is the mass of the club head, and m is the mass of the golf
The unknowns in the equations will be the final velocities of the
golf ball and club head, so first eliminate one of the final velocities
in equation 1 and substitute into equation 2.
3) Vf = vf - e(Vi
- vi) sub into equation 2
4) MVi + mvi = M[vf
- e(Vi - vi)] + mvf
Since the golf ball is originally at rest, vi
= 0, solving for final velocity of golf ball yields:
5) vf = [MVi(1 + e)]
/ (M + m)
Using similar algebra steps to solve for the final velocity of the
club head yields:
6) Vf = Vi(M - me) /
(M + m)
You can use these results and the fact that potential energy at the
collision point is equal to zero to calculate the energy lost in the
7) W = -(0.5MVf2 + 0.5mvf2
Click on Tiger Woods to see an example of the velocity of a Tiger
Woods drive and the energy lost to deformation of the ball.