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

Question

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

Infinity Learn · Accepted Answer

See fig. The resolved components of velocity v of the ball before and after striking the bat are shown in the figure. From figure, AF $$=$$ EB and. AE $$=$$ FB. The  velocity components EB and BD along the bat are equal in magnitude and are along the same direction.∴Change in momentum along the bat $$=mvsin$$⁡$$($$θ$$/2)$$−mvsin⁡$$($$θ$$/2)=0Now$$ impulse $$=$$ change in momentum along BF                    $$=mvcos$$⁡θ$$/2$$−$${$$−mvcos⁡θ$$/2}=2mvcos$$⁡$$($$θ$$/2)$$

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

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