A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed.  The system lies on a horizontal frictionless surface. The block is stretched by 0.2m and released from rest at t=0.  It then executes simple harmonic motion with angular frequency $\omega =\frac{\pi }{3}$  rad/s. Simultaneously at t=0, a small pebble is projected with speed v from point P at  an angle of  ${45}^0$ as shown in the figure. Point P is at a horizontal distance of $10m$  from O.  If the pebble hits the block at $t=1\sec ,$ the initial speed of pebble is $v=\sqrt{x}m/s.$  The value of x is (take g= 10 $m/s^2$)