Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.4 The Irrational Numbers - Exercise Set 5.4 - Page 298: 85

Answer

The aging rate of an astronaut is ${{R}_{a}}=0.44{{R}_{f}}$ and the astronaut is gone for 44weeks.

Work Step by Step

Substitute $v=0.9c$in Einstein’s special relativity equation and find ${{R}_{a}}$ $\begin{align} & {{R}_{a}}={{R}_{f}}\sqrt{1-{{\left( \frac{0.9c}{c} \right)}^{2}}} \\ & ={{R}_{f}}\sqrt{1-0.81} \\ & ={{R}_{f}}\sqrt{0.19} \\ & =0.44{{R}_{f}} \end{align}$ Now, use calculator to find $\sqrt{0.19}$ $\sqrt{0.19}=0.43588$ Now, substitute $100$ for ${{R}_{f}}$ and find ${{R}_{a}}$ $\begin{align} & {{R}_{a}}=100\times \left( 0.43588 \right) \\ & =43.588\approx 44 \end{align}$
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