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 0.2 m and released from rest at $\mathrm{t}=0$. It then executes simple harmonic motion with angular frequency $\omega=\frac{\pi}{3} \mathrm{rad} / \mathrm{s}$. Simultaneously at $\mathrm{t}=0$, a small pebble is projected with speed v from point P at an angle of $45^{\circ}$ as shown in the figure. Point P is at a horizontal distance of 10 cm from O . If the pebble hits the block at $t=1 \mathrm{~s}$, the value of v is $\left(\right.$ take $\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$