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.)

Explanation

Let I and j be unit vector in x and y direction respectively.
`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 in same direction magnitude but in opposite direction also hence they cancel each other in x- direction
compoment in y- direction
`Delta vec(p) =p_(2) cos theta - p_(1) cos theta (- j)`
`= p cos theta j + p cos theta hat(j) `
=2 ` cos theta `
Impulse of force on ball
`2 p cos theta `
` 2xx 0.15 xx 15 xx sin 67.5^(@)`
=`4.5 xx 0.9239`
Second Method

`p_(2) = mv[cos 45hat(j) + sin 45hat(j))`
`=mv [cos 45 + 1) hat(j ) = sin 45^(@) ]`
`=2.22 sqrt(1.707^(2)) + (0.707)^(2))`
`=4.2 N`