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 is fixed. The system lies on a horizontal frictionless surface. The spring is stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular frequency`omega=pi//3rad//s`. Simultaneously at t = 0, a small pebble is projected with speed v from point P 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=10m//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 phojectile
`T = (2usintheta)/(g) = 1` sec.
`(2usin45)/(g) = 1` sec : `u = (g)/(sqrt(2)) : u = sqrt(50) m//s`