Question 8: Why we can hit a long sixer in a cricket match rather than if we toss a ball ourselves?
Usually, a long sixer can be hit by the batsman instead of tossing the same ball by hand. A batsman while bating has the advantage of the momentum of the ball thrown by the bawler in comparison with one who just tosses by hand.
When we throw a ball by hand, we apply a force to the ball and produce a momentum in it. The ball goes in air exclusively by the force of the arm. When the batsman hits the ball, he is making use of the ball already has a momentum.
Let a batsman hits a ball of mass m coming towards him with a velocity vi and momentum p1 = mv1. He hits the ball so that it goes with a speed v2, momentum p2 = mv2. Change in momentum is,
If Δt is the time of contact of the bat and ball, then we know that rate of change of momentum equals the force applied. Therefore,
Compare both equations,
This equation gives the momentum of the ball after it is hit by the bat. On the right side, the first term is the initial momentum of the ball. Now, it clearly indicates that the final momentum of the ball is greater than the initial momentum by a factor, FavΔt which is a positive number (sometimes very small, otherwise quite large). Therefore, if a man tosses the ball by hand with a certain force and then hit the ball with the same force in a cricket match, the ball hit with the bat would have greater momentum. Thus, we can hit a long sixer in a cricket match rather than if we toss a ball ourselves