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

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 given by

Infinity Learn · Accepted Answer

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 Δ$$v=v$$′−$$v=v$$′$$+($$−$$v)$$, i.e.,∆V is the resultant of vectors v' and $$-v$$. As shown in figure, the magnitude of ∆V is given by Δ$$v=v2+v2+2v2cos$$⁡θ      $$=2v2(1+$$$$cos$$⁡θ$$)$$      $$=2v$$ $$cos$$ ⁡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 given by

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