First slide

Second law

Question

A ball of mass m is moving towards a batsman at a speed v. The batsman strikes the ball and deflects it by an angle $θ$ without changing its speed. The impulse imparted to the ball is

Easy

A

$mv \sin θ$
B

$mv \cos θ$
C

$2 mv \sin (θ / 2)$
D

$2 mv \cos (θ / 2)$

Solution

See fig. The resolved components of velocity v of the ball before and after striking the bat are shown in the figure. From figure, AF = EB and. AE = FB. The velocity components EB and BD along the bat are equal in magnitude and are along the same direction.
$∴$ Change in momentum along the bat
$= mvsin (θ / 2) - mvsin (θ / 2) = 0$
Now impulse = change in momentum along BF
$\begin{array}{l} = mvcos θ / 2 - {- mvcos θ / 2} \\ = 2 mvcos (θ / 2) \end{array}$

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