Respuesta :
Answer:
(A). The the time interval between signals according to an observer on A is 1.09 h.
(B). The time interval between signals according to an observer on B is 1.09 h.
(C). The speed is 0.866c.
Explanation:
Given that,
Time interval = 1.00 h
Speed = 0.400 c
(A). We need to calculate the the time interval between signals according to an observer on A
Using formula of time
[tex]\Delta t=\dfrac{\Delta t_{0}}{\sqrt{1-(\dfrac{v}{c})^2}}[/tex]
Put the value into the formula
[tex]\Delta t=\dfrac{1.00}{\sqrt{1-(\dfrac{0.400c}{c})^2}}[/tex]
[tex]\Delta t=\dfrac{1.00}{\sqrt{1-(0.400)^2}}[/tex]
[tex]\Delta t=1.09\ h[/tex]
(B). We need to calculate the time interval between signals according to an observer on B
Using formula of time
[tex]\Delta t=\dfrac{\Delta t_{0}}{\sqrt{1-(\dfrac{v}{c})^2}}[/tex]
Put the value into the formula
[tex]\Delta t=\dfrac{1.00}{\sqrt{1-(\dfrac{0.400c}{c})^2}}[/tex]
[tex]\Delta t=\dfrac{1.00}{\sqrt{1-(0.400)^2}}[/tex]
[tex]\Delta t=1.09\ h[/tex]
(C). Here, time interval of 2.00 h between signals.
We need to calculate the speed
Using formula of speed
[tex]\Delta t=\dfrac{\Delta t_{0}}{\sqrt{1-(\dfrac{v}{c})^2}}[/tex]
Put the value into the formula
[tex]2.00=\dfrac{1.00}{\sqrt{1-(\dfrac{v}{c})^2}}[/tex]
[tex]\sqrt{1-(\dfrac{v}{c})^2}=\dfrac{1.00}{2.00}[/tex]
[tex]1-(\dfrac{v}{c})^2=(\dfrac{1.00}{2.00})^2[/tex]
[tex](\dfrac{v}{c})^2=\dfrac{3}{4}[/tex]
[tex]v=\dfrac{\sqrt{3}}{2}c[/tex]
[tex]v=0.866c[/tex]
Hence, (A). The the time interval between signals according to an observer on A is 1.09 h.
(B). The time interval between signals according to an observer on B is 1.09 h.
(C). The speed is 0.866c.
