\[(a)\;3v\; \cos \theta \quad (b)\;2v\; \cos \theta \quad (c)\;v\; \cos \theta \quad (d)\;\frac{3}{2}v\; \cos \theta\]

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A shell fired at angle $'\theta'$ velocity of shell at highest point is $v \cos \theta$

Let its mass be m

speed of one piece $=v \cos \theta$

Let speed of other piece $=v'$

Using conservation of momentum

$mv \cos \theta=\large\frac{m}{2} $$ v \cos \theta+\large\frac{m}{2}v'$

Therefore $v'=3v \cos \theta$

Hence a is the correct answer.

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