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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