## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 5 - Number Theory and the Real Number System - 5.4 The Irrational Numbers - Exercise Set 5.4 - Page 298: 93

#### Answer

I would like to stay on earth because I want to live with my family and friends because when space traveler would come back to an unknown futuristic world the friends and loved ones would be long gone.

#### Work Step by Step

After a two-year journey to a futuristic world in which loved ones and friends are long gone. Einstein’s special relativity equation is as follows: ${{R}_{a}}={{R}_{f}}\sqrt{1-{{\left( \frac{v}{c} \right)}^{2}}}$ Here, ${{R}_{a}}$ represents rate by which the age of traveler increases,${{R}_{f}}$ represents the relative aging rate of a friend on earth, v is the speed of astronauts, and c is the speed of light. The equation described that the time would pass speedily on the Earth than time would pass in space. As v approaches the speed of light,then \begin{align} & {{R}_{a}}={{R}_{f}}\sqrt{1-{{\left( \frac{c}{c} \right)}^{2}}} \\ & ={{R}_{f}}\sqrt{1-{{\left( 1 \right)}^{2}}} \\ & ={{R}_{f}}\sqrt{0} \\ & =0 \end{align} Thus, nearby to the speed of light, the astronaut’s aging rate relative to a friend on Earth is zero. This implies when the people on Earth would be getting older the space traveler would barely get older. When space traveler would come back to an unknown futuristic world the friends and loved ones would be long gone. Hence, I would like to stay on earth because I want to live with my family and friends.

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