A sleeve of mass $m_1=5kg$ can slide on a smooth horizontal rod. A block of mass  $m_2=2kg$  is suspended at the midpoint of a light inextensible string of length $l= 2.3m,$ one end of which is attached to the sleeve and the other end is attached to one end of the rod. Initially the sleeve is held at the rest and the angle between the rod and a string segment is  ${\theta }_0={53}^0$ as shown in the figure. A constant horizontal force  $F=20N$ is applied on the sleeve. When the angle between the rod and the string segment becomes  $\theta ={37}^0$, the speeds of the sleeve and the block are  $v_{1}m/s \& v_{2}m/s$ respectively.