5.20 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.)

<p><picture><img src="https://images.shiksha.com/mediadata/images/articles/1728377923phpRMY1U3.jpeg" alt="" width="221" height="165"></picture></p><p>Velocity of the ball, u = 54 km/h = 15 m/s, mass of the ball, m = 0.15 kg</p><p>The ball is deflected back such that the included angle is 45&nbsp;<span title="Click to copy mathml"><math><mo>°</mo></math></span></p><p>The initial momentum of the ball, along the direction of NO is = mu&nbsp;<span title="Click to copy mathml"><math><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>? </mo><mrow><mi>θ</mi></mrow></mrow></math></span>&nbsp;= 0.15&nbsp;<span title="Click to copy mathml"><math><mo>×</mo></math></span>&nbsp;15&nbsp;<span title="Click to copy mathml"><math><mo>×</mo><mi></mi></math></span>&nbsp;cos 22.5&nbsp;<span title="Click to copy mathml"><math><mo>°</mo></math></span>&nbsp;= 2.0787 kg-m/s</p><p>The final momentum of the ball = mu&nbsp;<span title="Click to copy mathml"><math><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>? </mo><mrow><mi>θ</mi></mrow></mrow></math></span>&nbsp;along ON</p><p>Impulse = change of momentum = mu&nbsp;<span title="Click to copy mathml"><math><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>? </mo><mrow><mi>θ</mi></mrow></mrow></math></span>&nbsp;- (-mu&nbsp;<span title="Click to copy mathml"><math><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>? </mo><mrow><mi>θ</mi></mrow></mrow></math></span>&nbsp;) = 2mu&nbsp;<span title="Click to copy mathml"><math><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>? </mo><mrow><mi>θ</mi></mrow></mrow></math></span>&nbsp;= 4.16 kg-m/s</p>

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