When traveling past an observer with a relative speed v, a rocket is measured to be 9.10 m long. when the rocket moves with a relative speed 2v, its length is measured to be 4.90 m?

This is a consequence of special relativity.

The equation to calculate this 'length contraction' is below but you would need more information than you have given to work it out.

L' = L x sqrt(1 - (v^2)/(c^2))

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