Catching and batting - a further example of the vector nature of momentum

When you catch a ball of mass m that was travelling at velocity v the change of momentum of the ball during the catching is mv. To do this you must apply a force F for a time t. So since impulse equals change of momentum Ft = mv. You can see that the longer you take to bring the ball to rest the smaller the force - that's why it is sensible to "bring your hands back" when catching a ball - especially a hard one like a cricket ball, the ball does not "give" so you must.



When you hit the ball straight back the change of momentum is much bigger.

Momentum of ball before collision = mv
Momentum of ball after collision = - mv [momentum is a vector and we must allow for the change of direction, the minus sign tells you that the ball is moving in the opposite direction].

Therefore change of momentum of ball = mv - (-mv) = 2mv

So force on the ball F = 2mv/t and if the time spent in hitting the ball backwards is the same as that spent in catching you can see that the force will be twice as large.