Two particles A and B of equal mass M are moving with the same...

After inelastic collision mass of the combination is& $\text{2m}$

$v '$~be the velocity of the combined mass

Using conservation of momentum along& $X$~and $Y$-axis

$2mv^{′}sin \theta = \dfrac{mv}{2} + \dfrac{mv\sqrt{3}}{2}$

$2mv^{′}cos \theta = \dfrac{mv}{2} - \dfrac{mv}{2}$

$\dfrac{2sin \theta}{2cos \theta} = \dfrac{\dfrac{1}{2} + \dfrac{3}{2}}{\dfrac{1}{2} - \dfrac{1}{2}} = \dfrac{\sqrt{2} + \sqrt{3}}{1 - \sqrt{2}}$

$tan\theta = \dfrac{\sqrt{2} + \sqrt{3}}{1 - \sqrt{2}}$