Question

How far the rocket have to go relative to an observer for its length to be contracted to 99 percent of its length at rest

Answer 1

We will apply special relativity here,

γ = 1/√(1–V²/c²)

so, here, γ= original length / length after contraction=1/0.99

=> 1/0.99=1/√(1–V²/c²)

1–V²/c²=0.9801

V²/c²=0.0199

V/c=0.141

=141/100= (14.1%)c

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Answer 2

γ = 1/√(1–V²/c²)  

so, here, γ= original length / length after contraction=1/0.99

=> 1/0.99=1/√(1–V²/c²)

1–V²/c²=0.9801

V²/c²=0.0199

V/c=0.141

=141/100= (14.1%)c

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