Question

You fly your 15 m spaceship, parallel to the ship's length with a speed of c/3 relative to your friend. How long is your spaceship as observed by your friend?

Answer 1

We are asked to determine the length of a ship whose length is 15 meters. To determine the relative length we will use the following formula:

$L=L_0\sqrt{1-\frac{v^2}{c^2}}$

Where:

$\begin{gathered} L=\text{ relative length} \\ L_0=\text{ original length} \\ v=\text{ velocity of the object} \\ C=\text{ speed of light} \end{gathered}$

Now, we substitute the value of the speed as a function of the speed of light:

$v=\frac{c}{3}$

Substituting we get:

$L=L_0\sqrt{1-\frac{(\frac{c}{3})^2}{c^2}}$

Now, we distribute the exponent and simplify:

$L=15m\sqrt{1-\frac{1}{9}}$

Solving the operations:

$L=14.14m$

Therefore, the length of the spaceship observed by the friend is 14.14 meters.