Answer:
A)
0.8 c
B)
0.87 c
Explanation:
A)
L₀ = Original length of the meter stick = 1 m
L = Length observed = 0.6 m
[tex]v[/tex] = speed of the meter stick
Using the equation
[tex]L = L_{o} \sqrt{1 - \left ( \frac{v}{c} \right )^{2}}[/tex]
[tex]0.6 = 1 \sqrt{1 - \left ( \frac{v}{c} \right )^{2}}[/tex]
[tex]0.36 = 1 - \left ( \frac{v}{c} \right )^{2}[/tex]
[tex]v[/tex] = 0.8 c
B)
T₀ = Time of the clock at rest = t
T = Time of the clock at motion = (0.5) t
[tex]v[/tex] = speed of the clock
Using the equation
[tex]T = T_{o} \sqrt{1 - \left ( \frac{v}{c} \right )^{2}}[/tex]
[tex]0.5 t = t \sqrt{1 - \left ( \frac{v}{c} \right )^{2}}[/tex]
[tex]0.5 = \sqrt{1 - \left ( \frac{v}{c} \right )^{2}}[/tex]
v = 0.87 c
