Two particles $P$ and $Q$ start their journey simultaneously from point $A$. $P$ moves along a smooth horizontal circular wire with diameter $AB$. $Q$ moves along a curved smooth track. $Q$ has sufficient velocity at $A$ to reach $B$ always remaining in contact with the curved track. At $A$, the horizontal component of velocity of $Q$ is same as the velocity of $P$ along the wire. The plane of motion is vertical. If $t_1,t_2$, are times taken by $P$ and $Q$ respectively to reach $B$ then (Assume velocity of $P$ is constant)