Question

How fast would a rocket have to go relative to an observer for its lenght to be contracted to 99 percent of its lenght at rest.

Answer 1

Hi friend,
Your answer is in the attachment.

Hope this helped you a little!!!

Answer 2

Answer:

Required velocity of rocket is $=0.42*10^8m/s$

Explanation:

Let the proper length of the rocket be $l_o$;

Contracted length is given by, $l=l_o\sqrt{1-\frac{v^2}{c^2} }$ ----(1)

where, $v$ is the velocity of the rocket,

and $c$ is the speed of light = $3*10^8m/s$

Given : contracted length = 99% of $l_o$ = $\frac{99}{100} l_o$ ----(2)

Equating (1) and (2)

$\frac{99}{100} l_o=l_o\sqrt{1-\frac{v^2}{c^2} }$

$\implies (\frac{99}{100})^2 =1-\frac{v^2}{c^2} }$

$\implies \frac{v}{c } =\sqrt{1- (\frac{99}{100})^2}$

$\implies v = 0.14c$

$\implies v=0.14*3*10^8m/s$

$\implies v=0.42*10^8m/s$

Required velocity of rocket is $=0.42*10^8m/s$

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