Question

The diameter of the solar system is $10$light hours. A spaceship crosses the solar system in$15$ hours, as measured on earth. How long, in hours, does the passage take according to passengers on the spaceship?

Short answer

In hours $11.18hr$does the passage take according to passengers on the spaceship.

Step-by-step solution

Given Information 

We need to find time, in hours, does the passage take according to passengers on the spaceship.

Simplify

The rocket's velocity is given as :

$v=\frac{10}{15}c=2\times {10}^{8}m/s$

So, the time measured from earth is :

$$\begin{gathered} t\text{'}=t\sqrt{1-\left(\frac{v^2}{u^2}\right)} \\ t\text{'}=15\sqrt{1-\frac{{\left(2\times {10}^8\right)}^2}{{\left(3\times {10}^{8}m/s\right)}^2}} \\ t\text{'}=15\times 0.74565 \\ t\text{'}=11.18hr \end{gathered}$$