Explanation:
It is given that,
Speed of the person, v = 3 mile/hr = 1.34 m/s
Speed of the truck, v' = 65 mile/hr = 29.05 m/s
(a) Since, [tex]\beta =\dfrac{v}{c}[/tex]
For the person, [tex]\beta =\dfrac{1.34}{3\times 10^8}=4.47\times 10^{-9}[/tex]
For the truck, [tex]\beta =\dfrac{29.05}{3\times 10^8}=9.68\times 10^{-8}[/tex]
(b) The relativistic factor is given by :
[tex]\gamma=\dfrac{1}{\sqrt{1-\beta^2}}[/tex]
For very small velocity, [tex]\beta<<1[/tex]
[tex]\gamma=(1-\beta ^2)^{-1/2}\approx 1+\dfrac{1}{2}\beta ^2[/tex]
[tex]\gamma-1=\dfrac{\beta^2}{2}[/tex]
For the person :
[tex]\gamma-1=\dfrac{(4.47\times 10^{-9})^2}{2}=9.99\times 10^{-18}[/tex]
For the person :
[tex]\gamma-1=\dfrac{(9.68\times 10^{-8})^2}{2}=4.68\times 10^{-15}[/tex]
Hence, this is the required solution.
