Question

A pion is an unstable particle that has a mean lifetime of 2.55 × 10-8 s. This is the time interval between its creation in a nuclear process and its extinction into decay products, as measured in a frame of reference at rest with respect to the pion. An average pion is traveling at 0.230c relative to Earth. How far does it travel in its lifetime, relative to Earth?

Answer 1

`\large \boxed{\text{1.76 m}}`

Step-by-step explanation:

Data:

Lifetime = 2.55 × 10⁻⁸ s

Speed = 0.230c

Calculations:

`\text{Speed} = \text{0.230c} = 0.230 * \frac{\text{2.998 $* 10^(8)$ m}}{\text{1 s}} = 6.895 * 10^(7)\text{ m/s }\\\\\begin{array}{rcl}\text{Distance} & = & \text{speed $*$ time}\\& = & \frac{6.895 * 10^(7)\text { m}}{\text{1 s}} * 2.55 * 10^(-8)\text{ s}\\\\& = & \textbf{1.76 m}\\\end{array}\\\text{The pion travels $\large \boxed{\textbf{1.76 m}}$ in its lifetime.}`