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Fastest bowling in cricket history is Shoaib Akhtar's 161.3 km/h.

From Google.

Then what was the speed of his arm when he delivered the cricket ball to the pitch? Is it possible to tell? Hand cannot move that fast can it?

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It isn't possible, from the information provided, to tell what speed various parts of his arm are moving at. But what can be confirmed is that the part of his arm in contact with the ball before it is released (presumably the tips of his fingers) is travelling at a minimum speed of 161.3 km/h. In practice, if he imparts any spin at all to the ball, then the tips of his fingers are likely moving somewhat faster.

The only way in which it would be possible for an 'arm' to be moving slower than the ball would be if, at some stage during the bowling motion, the bowlers hand lost contact with the ball and then struck it from behind. In theory, the ball could then 'rebound' forwards faster then the moving hand (somewhat in the way that a tennis ball moves faster than the racquet during a serve): in practice, I don't think that such a motion would be physiologically possible (or legal within the game).

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Yes, the speed of the ball at the time of release will be equal to the speed of the part of the hand in contact with the ball. So, in case of a cricket bowler, the part of the bowler's fingers that are in contact with the ball at the time of release will be moving that fast.

This may seem unbelievable but it is possible because the end of the hand is one end of a long lever i.e. the arm. So, the end can move that fast, atleast for that brief instant. Think of how you can move the end of a towel to supersonic speeds by giving it that whip.

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