When you are driving a golf ball,a good follow-through helps to increase the distance of the drive. A good follow-through means that the club head is kept incontact with the ball as long as possible.Why does this technique allow you to hit the ball farther ?

Answer 1

The larger contact time means longer duration of the impulse imparted to the golf ball. (Impulse I = F*t)
Largere impulse causes larger change in the momentum of the ball. And the distance covered is directly proportional to the momentum imparted.