A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54

Question

A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the magnitude of the impulse imparted to the ball? (Mass of the ball is 0.15 kg)

Professor PC Thomas Classes · Answer

Speed $v = 54$ km/h $= 15$ m/s. Initial momentum $p_1 = mv = 0.15 	imes 15 = 2.25$ kg m/s. Final momentum $p_2 = 2.25$ kg m/s. Change in momentum $\Delta p = \sqrt{p_1^2 + p_2^2 - 2p_1 p_2 \cos 45^\circ} = 2.25 \sqrt{2 - \sqrt{2}} \approx 2.25 	imes 0.765 = 1.72$ N s.