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.

Explanation

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))`