Question

How fast does a rocket ship have to go for its length to be contracted to 99% of its rest length?

Answer 1

4.2×10⁷ m/s

Step-by-step explanation:

L = length observed by an observer

L₀ = Proper length

v = Velocity of the rocket ship

Length contraction formula

`L=L_(0){\sqrt{1-(v^(2))/(c^(2))}}\\\Rightarrow 0.99=1{\sqrt{1-(v^(2))/(c^(2))}}\\\Rightarrow (0.99)/(1)={\sqrt{1-(v^(2))/(c^(2))}}\\\Rightarrow 0.99^2=1-(v^(2))/(c^(2))\\\Rightarrow 0.99^2-1=-(v^2)/(c^2)\\\Rightarrow 0.0199* c^2=v^2\\\Rightarrow v=√(0.0199)c=v\\\Rightarrow v =√(0.0199)* 3* 10^8\\\Rightarrow v=4.2* 10^7\ m/s`

The speed of the ship would be 4.2×10⁷ m/s