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 `nu` from point P at an angle of `45^(@)` as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at t = 1s, the value of `nu` is (take g = 10 m/`s^(2)` )

Options

A. `sqrt(50)m//s`
B. `sqrt(51)m//s`
C. `sqrt(52)m/s`
D. `sqrt(53)m/s`

Answer

A

Explanation

Time of flight for projectile
`T=(2usintheta)/(g)=1sec`, `(2usin45)/(g)=1sec`, `u=(g)/(sqrt2)`, `u=sqrt(50)m//s`.