Is this JEE mechanics problem incomplete due to missing assumptions? [closed]

I came across the following JEE problem:

A bead $P$ slides without friction on a semicircular wire $ACB$. At $t=0$, it is at point $S$, and the horizontal component of its velocity is $v$. Another bead $Q$ is projected from $A$ along the horizontal wire $AB$ with speed $v$. Neglect any friction between the beads and the wires. Let $t_P$ and $t_Q$ denote the times taken by the beads to reach $B$. Compare $t_P$ and $t_Q$.

I believe the problem is missing some essential assumptions.

Plane of motion

The orientation of the plane containing the semicircular wire is never specified. If the wire lies in a horizontal plane, gravity has no tangential component, so bead $P$ moves with constant speed. If it lies in a vertical plane, gravity continuously changes the bead's speed, leading to a completely different analysis. The statement only mentions the horizontal component of the velocity, which by itself does not uniquely determine the orientation of the wire.

Can bead $P$ even reach $B$?

Even if a vertical plane is intended, the problem does not appear to guarantee that bead $P$ actually reaches $B$.

From the given information, the initial speed of bead $P$ is

$
u=\sqrt{2}\,v.
$

Applying conservation of mechanical energy, bead $P$ can reach $B$ only if

$
\frac{1}{2}m(\sqrt{2}v)^2 \ge mg\left(\frac{R}{\sqrt{2}}\right),
$

which simplifies to

$
v^2 \ge \frac{gR}{\sqrt{2}},
$

where $R$ is the radius of the semicircular wire.

If this condition is not satisfied, the bead would come to rest before reaching $B$, making $t_P$ undefined.