A batsman deflects a ball by an angle of 45^(@) without changing its initial speed which is equal to 36 km/h. what is the impulse imparted to the ball? Given, mass of ball is 0.157 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 36 km/h. what is the impulse imparted to the ball? Given, mass of ball is 0.157 kg.
Answer» Solution :Let initial velocity of the ball is `vec(v_(1))` and FINAL velocity of the ball is `vec(v_(2))`. `therefore` Impulse,`vec(I) = m(vec(v_(2)) - vec(v_(1)))` [ m = mass of the ball ] Magnitude of initial and final velocities are the same, i.e., `\|vec(v_(1))\| = \|vec(v_(2))\| = 36km CDOT h^(-1)` `"" = (36 xx 10^(3))/(3600) m cdot s^(-1)` `"" 10 m cdot s^(-1)` From FIGURE, `\|vec(v_(2)) - vec(v_(1))\| = sqrt( v_(1)^(2) + v_(2)^(2) + 2v_(1)v_(2) cos 45^(@))` `= sqrt(10^(2) + 10^(2) + 2 xx 10 xx 10 xx (1)/(sqrt(2)))` `approx` 18.5 m`cdot s^(-1)` `therefore ""\|vec(I)\| = m\|vec(v_(2)) - vec(v_(1))\|` = 0.157 `xx 18.5 "kg" cdot m cdot s^(-1) = 2.9 "kg" cdot m cdot s^(-1)` The direction of imparted impulse is ALONG bisector of the angle between `vec(v_(2)) and - vec(v_(1))`