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# A shell is fired from a canon with a velocity v at an angle $\theta$ with the horizontal. At the highest point of its path it explodes into two pieces of equal masses, one of the pieces retraces its path to point of throw. what is speed of second piece immediately after explosion

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

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.
edited Jun 5, 2014