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 $$=$$ $$0$$. It then executes simple harmonic motion with angular frequency ω$$=$$π$$3$$ $$radian/s$$.Simultaneously, at t $$=$$ $$0$$, a small pebble is projected with speed ‘v’ from point ‘P’ at an angle of $$450$$ as shown in the figure. point P is at a horizontal distance of $$10m$$ from O. If the pebble hits the block at t $$=$$ $$1sec$$, the value of ‘v’ is : (take$$ g $$=$$ $$10m/s2)

Question

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 $$=$$ $$0$$. It then executes simple harmonic motion with angular frequency ω$$=$$π$$3$$ $$radian/s$$.Simultaneously, at t $$=$$ $$0$$, a small pebble is projected with speed ‘v’ from point ‘P’ at an angle of $$450$$ as shown in the figure. point P is at a horizontal distance of $$10m$$ from O. If the pebble hits the block at t $$=$$ $$1sec$$, the value of ‘v’ is : (take$$ g $$=$$ $$10m/s2)

Infinity Learn · Accepted Answer

As the pebble hits the block at  t $$=$$ $$1$$ $$sec$$., hence $$2vsin45$$∘$$g=1$$ ∴$$v=50m/s$$

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