A ball of mass m is moving towards a batsman at a speed v. The batsman strikes the ball and deflects it by an angle θ without changing its speed. The impulse imparted to the ball is given by

The ball moving along AB with velocity v is deflected along BC with velocity v'. The magnitude of vectors v and v' is the same = v.Change in velocity is Δv=v′−v=v′+(−v), i.e.,∆V is the resultant of vectors v' and -v. As shown in figure, the magnitude of ∆V is given by Δv=v2+v2+2v2cos⁡θ      =2v2(1+cos⁡θ)      =2v cos ⁡θ2