First slide

Newton's laws of motion

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 given by

Moderate

A

$mv \cos (θ)$
B

$mv \sin (θ)$
C

$2 mv \cos (\frac{θ}{2})$
D

$2 mv \sin (\frac{θ}{2})$

Solution

The ball moving along AB with velocity v is deflected along BC with velocity v'. The magnitude of vectors v and v' is the same = v.
Change in velocity is $Δ v = v^{'} - v = v^{'} + (- v)$ , i.e., $∆ V$ is the resultant of vectors v' and -v. As shown in figure, the magnitude of $∆ V$ is given by
$Δv = \sqrt{v^{2} + v^{2} + 2 v^{2} \cos θ} = \sqrt{2 v^{2} (1 + \cos θ)} = 2 v \cos (\frac{θ}{2})$

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