Answer
$(a)$ Along the $+y$ direction
Work Step by Step
According to law of conservation of momentum
$initial$ $momentum=final$ $momentum$
for y
$E/C+0=mv+E'sin\theta/C$
for x
$0=Ecos\theta/C+0$
$cos\theta=0$
$\theta=90^{\circ}$
So, scattered photon move in $+y$ direction
