Answer:
The time interval is 22.76 hr.
Explanation:
Given that,
Time = 30 hrs
Speed = 0.74c
We need to calculate the time interval measured in earth frame
Using formula of time dilation
[tex]\Delta t=\dfrac{\Delta t_{0}}{\sqrt{1-\dfrac{v^2}{c^2}}}[/tex]
Where, [tex]\Delta t[/tex] = time interval measured in earth frame
[tex]\Delta t_{0}[/tex]=proper time interval
Put the value into the formula
[tex]\Delta t=\dfrac{30}{\sqrt{1-\dfrac{0.74c^2}{c^2}}}[/tex]
[tex]\Delta t=\dfrac{30}{\sqrt{1-(0.74)^2}}[/tex]
[tex]\Delta t=\dfrac{30}{0.6726}[/tex]
[tex]\Delta t=44.60\ hr[/tex]
We need to calculate the proper time interval when the velocity is 0.86c
Using formula of time dilation
[tex]44.60=\dfrac{\Delta t_{0}}{\sqrt{1-\dfrac{0.86c^2}{c^2}}}[/tex]
[tex]\Delta t_{0}=44.60\times\sqrt{1-(0.86)^2}[/tex]
[tex]\Delta t_{0}=22.76\ hr[/tex]
Hence, The time interval is 22.76 hr.
