d
\(\begin{array}{l}
According\,to\,law\,of\,conservation\,of\\
linerar\,momentum\,along\,x - axis,\,we\,get\\
{m_1} \times 0 + {m_2} \times v = {m_1}v'\cos \theta \\
{m_2}v = {m_1}v'\cos \theta \\
or\,\cos \theta  = \frac{{{m_2}v}}{{{m_1}v'}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\\
According\,to\,law\,of\,conservation\,of\,\\
linear\,momentum\,along\,y - axis,\,we\\
get
\end{array}\)

\(\begin{array}{l}
{m_1} \times 0 + {m_2} \times 0 = {m_1}v'\sin \theta  + {m_2}\frac{v}{2} - {m_2}\frac{v}{2}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {m_1}v'\sin \theta \\
\sin \theta  =  - \frac{{{m_2}v}}{{2{m_1}v'}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)\\
Divide\,\left( {ii} \right)\,by\,\left( i \right),\,we\,get\\
\tan \theta  =  - \frac{1}{2}\,or\,\theta  = {\tan ^{ - 1}}\left( { - \frac{1}{2}} \right)\,to\,the\,x - axis
\end{array}\)