A uniform sphere is given an angular velocity \(\omega = 7\text{ rad/sec}\) in the clockwise direction and is released from a height \( h = 22\text {m}\) towards the rough ground .

It collides with the sufficiently rough ground and rebounds with it at an angle \(\theta \).

Find the range of the projectile thus traced (before next collision)

**Details and Assumptions**:

Radius of sphere is \( R = 2\text{ m}\), \( g = 10\text{ m/s}^2\).

It's velocity in the vertical direction is reduced by 5 times(due to collision).

Ground has sufficient friction such that when sphere is on ground it is in the state of pure rolling.I.e. before rebounding the sphere has already started pure rolling.

The initial height measured is of Centre of mass of sphere from ground.

Neglect air drag, bouancy effect . Neglect all deviation effects on the rotating sphere (due to rotation) when in air.

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