Answer:
The speed of the observer is 2.4 x 10^8 m/s
Explanation:
The standard length of a meter stick is 100 cm
we are to calculate at what speed parallel to the length the length reduces to 60 cm.
This is a relativistic effect question. We know that the length will contract to this 60 cm following the equation below
[tex]l = l_{0}\sqrt{1 - \beta ^{2} }[/tex]
where
[tex]l[/tex] is the new length of 60 cm
[tex]l_{0}[/tex] is the original length which is 100 cm
[tex]\beta[/tex] is the the ratio v/c
where
v is the speed of the observer
c is the speed of light = 3 x 10^8 m/s
substituting values, we have
60 = [tex]100\sqrt{1 - \beta ^{2} }[/tex]
0.6 = [tex]\sqrt{1 - \beta ^{2} }[/tex]
we square both side
0.36 = 1 - [tex]\beta ^{2}[/tex]
[tex]\beta ^{2}[/tex] = 1 - 0.36 = 0.64
β = [tex]\sqrt{0.64}[/tex] = 0.8
but β = v/c
v/c = 0.8
substituting value of c, we have
v = 0.8 x 3 x 10^8 = 2.4 x 10^8 m/s
