Q6PE - College Physics (Urone)

Question

A neutron lives 900 s when at rest relative to an observer. How fast is the neutron moving relative to an observer who measures its life span to be 2065s?

Step-by-Step Solution

Answer

The neutron is moving relative to an observer at the velocity of  900 c.

 

Step 1: To find the velocity

The life of the neutron when relative to an observer i.e., proper time is 

∆t₀ = 900s

The life of the neutron when measured in the laboratory

∆t = 2065 s

we have

_{\[\Delta t = \frac{{\Delta {t_0}}}{{\sqrt {1 - {{\left( {\frac{v}{c}} \right)}^2}} }}\]}                             - (1)

 

Where v is its velocity relative to an observer and c = 3.00 × 10⁸ ms^-1 is the speed of the light 

Step 2: To solve the equation

From the above equation (1), we get

\begin{aligned}v = c\sqrt {1 - {{\left( {\frac{{\Delta {t_0}}}{{\Delta t}}} \right)}^2}} \\= c\sqrt {1 - {{\left( {\frac{{900s}}{{2065s}}} \right)}^2}} \\= 0.900c\end{aligned}

Hence the neutron moving relative to an observer in the velocity of v = 0.900 c .