A river of width $\omega$ is flowing with a uniform velocity $v$. A boat starts moving from point $P$ also with velocity $v$ relative to the river. The direction of resultant velocity is always perpendicular to the line joining boat and the fixed point $R$. Point $Q$ is on the opposite side of the river. $P,Q$ and $R$ are in a straight line. If $PQ=QR=\omega$, find the trajectory of the boat.