Simple Harmonic Motion

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 t = 0. It then executes simple harmonic motion with angular frequency \(\omega\) = (\(\pi\)/3) rad/s. Simultaneously, at 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 O is at a horizontal distance of 10 m from O. If the pebble hits the block at t = 1 s, the value of v is (take g = 10 m/s²)