A particle of mass m is projected with velocity v at an angle θ...

A particle of mass

m

is projected with velocity

v

at an angle

\theta

with the horizontal. At its highest point, it explodes into two pieces of equal mass, one of the piece continue to move on the original trajectory, then the velocity of second piece is

Options

A $2 v \cos \theta$
B $v \cos \theta$
C $3 v \cos \theta$
D $\frac{v}{2} \cos \theta$

Correct answer

B. $v \cos \theta$

Step-by-step solution

According to the law of conservation of linear momentum at the highest point, m v \cos

\theta=\frac{m}{2}(v \cos \theta)+\frac{m}{2}

v^{\prime}

\Rightarrow \quad m v \cos \theta-\frac{m}{2} v \cos \theta=\frac{m}{2} v^{\prime}\Rightarrow \quad v^{\prime}=2\left(v \cos \theta-\frac{v \cos \theta}{2}\right)=v \cos \theta

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