# Rolling Projectile!

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.

This question is original.

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