According to an observer on Earth, a spacecraft whizzing by at 0.6c is 35 m long. What is the length of the spacecraft according to the passengers onboard?

Length contraction is the phenomenon where a moving object’s length is measured to be shorter than its proper length.Hence, the length of spacecraft according to an observer on earth will be shorter than its original length according to the passengers on board.

Length contraction is given by

$l=l_0\sqrt{1-\frac{v^2}{c^2}}$

Velocity of spacecraft$\left(V\right)=0.6cm/s$

Length of spacecraft according to an observer on earth$\left(l\right)=35m$

Speed of light(c) = $3\times {10}^8\text{m/s}$

We have to find,

Length of spacecraft according to observer onboard$\left(l_{\circ }\right)$

When we use the formula from step 1 and rearrange it in terms of known values, we get the following,

$\begin{array}{l}l=l_{\circ }\sqrt{1-\frac{v^2}{c^2}}\\ l_{\circ }=\frac{l}{\sqrt{1-\frac{v^2}{c^2}}}\\ l_{\circ }=\frac{35m}{\sqrt{1-\frac{{\left(0.6c\right)}^2}{c^2}}}\\ l_{\circ }=\frac{35m}{\sqrt{1-{\left(0.6\right)}^2}}\end{array}$

Simplifying further,

$\begin{array}{l}{l}_{\circ }=\frac{35m}{\sqrt{0.64}}\\ l_{\circ }=\frac{35m}{0.8}\\ l_{\circ }=43.75m\end{array}$

Hence, the original length of the spacecraft is.$43.75\text{\hspace{0.17em}m}$