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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 impulse imparted to the ball ? (Mass of the ball is 0.15 kg.)

Q5.20    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 impulse imparted to the ball? (Mass of the ball is 0.15 kg.)

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The situation is shown below :

                                   

The horizontal components of velocity are to be considered for imparting impulse as vertical components are in the same direction thus impulse in the vertical direction is zero.

The impulse is given by change in momentum.

                Initial momentum   =     -mv \cos \Theta

               Final momentum    =         mv \cos \Theta

Thus impulse is         =\ mv \cos \Theta\ -\ (-\ mv \cos \Theta)\ =\ 2mv \cos \Theta

or                              =\ 2\times0.15 \times15\ \cos 22.5 ^{\circ}

or                              =\ 4.16\ Kg\ m/s

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