A small block is connected to one end of a massless spring of unstretched 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. lt then executes simple harmonic motion with angular frequency $ω = \frac{π}{3} r a d / s$ .
Simultaneously at t=0, a small pebble is projected with speed v 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 = 1 s, the value of v is
(take $g = 10 m / s^{2}$ )

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Answer 1

Time is given by $t = \frac{2 v s i n θ}{g}$
$1 = \frac{2 v s i n 4 5 ^{o}}{1 0}$
$v = 50 m / s$

Answer 2

Time is given by

t = \frac{2 v s i n θ}{g}

1 = \frac{2 v s i n 4 5 ^{o}}{1 0}

v = 50 m / s