Solution Found!
When he returns his Hertz rent-a-rocket after one week's
Chapter 15, Problem 15.6(choose chapter or problem)
When he returns his Hertz rent-a-rocket after one week's cruising in the galaxy, Spock is shocked to be billed for three weeks' rental. Assuming that he traveled straight out and then straight back, always at the same speed, how fast was he traveling? (See note to 15.5.)
Questions & Answers
QUESTION:
When he returns his Hertz rent-a-rocket after one week's cruising in the galaxy, Spock is shocked to be billed for three weeks' rental. Assuming that he traveled straight out and then straight back, always at the same speed, how fast was he traveling? (See note to 15.5.)
ANSWER:Step 1 of 2
\(\frac{\Delta t^{\prime}}{\Delta t}=\sqrt{1-\beta^{2}}\)
Where, \(\Delta t^{\prime}=1\) and \(\Delta t=3\)
That is,
\(\frac{1}{3}=\sqrt{1-\beta^{2}}\)
Implies,
\(\beta^{2}=1-\frac{1}{9}=\frac{8}{9}\)
So,
\(\begin{array}{l} \beta=\sqrt{\frac{8}{9}} \\ \beta=\frac{2 \sqrt{2}}{3}\ldots\ldots(1) \end{array}\)