\[(a)\;4\; m/s; 45 ^{\circ} \quad (b)\;6\; m/s; 45 ^{\circ} \quad (c)\;4\; m/s; 90 ^{\circ} \quad(d)\;6\; m/s; 90 ^{\circ} \]

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We use conservation of kinetic energy as we cannot use conservation of linear momentum as direction of the ball after collision is not known

KE before collision $=\large \frac{1}{2} $$m .10 ^2+0$

$\qquad=50 \;mJ$

KE after collision $=\large \frac{1}{2} $$m \times 8 ^2+\large\frac{1}{2}$$ m \; v^2$

$\qquad=(32 +\large\frac{1}{2}$$mv^2)J$

$32\;m+\large\frac{1}{2}$$mv^2=50 m$

$v^2=36$

$v=6$$ m/s$

Since we see that $10^2=8^2+6^2$

The two balls must be moving at right angles to each other.

Hence d is the correct answer

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