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.)

A batsman deflects a ball by an angle of 45^(@) without changing its i

1.	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.)
Answer» Solution :LetI andjbe unitvectorin X and y directionrespectively. `P_(1)= mv_(1)` `p_(2) = mv_(2)` and `theta= (45^(@))/( 2) =22.5^(@)` HENCE `p_(1) cos theta ` and `p_(2)cos theta`are insamedirectionmagnitudebut in oppositedirectionalsohencetheycanceleachotherin x-direction compomentin y- direction `Delta vec(p)=p_(2)cos theta- p_(1) cos theta (- j)` `= p costheta j +p costheta HAT(j) ` =2 ` cos theta ` Impulseofforceon ball `2 p cos theta` ` 2xx0.15xx 15 xxsin67.5^(@)` =`4.5xx 0.9239` SecondMethod `p_(2)= mv[cos 45hat(j)+ sin45hat(j))` `=mv [cos45 +1) hat(j )= sin 45^(@) ]` `=2.22 sqrt(1.707^(2)) + (0.707)^(2))` `=4.2 N`