Question

I need help with a time dilation and length contraction worksheet

Answer 1

Given:

The speed of the spaceship, v=0.75c

The time elapsed on the earth Δt₀=45 years=1.42×10⁹ s

To find:

The age of the twin that was sent into space.

Step-by-step explanation:

The age of the twin sent into space is given by,

`\Delta t_0=\frac{\Delta t}{\sqrt{1-(v^2)/(c^2)}}`

On substituting the known values,

`\begin{gathered} 1.42*10^9=\frac{\Delta t}{\sqrt{1-(0.75^2* c^2)/(c^2)}} \\ \implies\Delta t=1.42*10^9*√(1-0.75^2) \\ =0.94*10^9\text{ s} \end{gathered}`

Converting it to years,

`\Delta t=0.94*10^9\text{ s}=29.8\text{ years}`

Final answer:

Thus the age of the twin that was sent into space is 29.8 years