The force of the Bowling ball colliding with the Golf ball causes the golf ball to be redirected in an elastic collision. How fast either travels depends on the friction of the surface and the angle of contact with the bowling ball.
Comparative Masses and Energy
In the collision between a golf ball and a bowling ball, the fact that the bowling ball continues to move (although possibly changed in direction) is a function of the comparative masses of the two. The bowling ball is much more massive, so at normal velocities its kinetic energy exceeds the kinetic energy of the golf ball. In order to "stop" the bowling ball, the golf ball would have to make a perfectly aimed collision, and have a much higher velocity. Quantitatively, the velocity of the golf ball would have to be the inverse ratio of the ratio of the masses of the two balls, so that the kinetic energy (mass times velocity) is equal and in the opposite direction.
Example : Golf ball at 45 g, ten pound bowling ball at 4500 g -- the golf ball would have to move at 100 times the velocity of the bowling ball to counteract its kinetic energy. If the bowling ball rolls at 2 m/sec, the golf ball would have to travel at more than 200 m/sec (720 kph or 447 mph), about 3 times a ball's normal velocity off the face of a golf club.
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