Quick check from College Physics, 28.2 Simultaneity And Time Dilation

Simultaneity And Time Dilation: quick check

1. What is $γ$ if $v = 0 .650 c$ ?

2. A particle travels at $1 . 90 \times 10^{8} m/s$ and lives $2 . 10 \times 10^{- 8} s$ when at rest relative to an observer. How long does the particle live as viewed in the laboratory?

Answer it in your own words before you look.

Answer
1. $γ = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{1}{\sqrt{1 - \frac{(0.650 c)^{2}}{c^{2}}}} = 1 . 32$

2. $Δ t = \frac{{Δ t}_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{2 . 10 \times 10^{- 8} s}{\sqrt{1 - \frac{(1 . 90 \times 10^{8} m/s)^{2}}{(3 . 00 \times 10^{8} m/s)^{2}}}} = 2 . 71 \times 10^{- 8} s$

How did it go?