Answer:
The length of the stick is 0.28 m.
The time the stick take to move is 0.97 ns.
Explanation:
Given that,
Relative speed of stick v= 0.96 c
Speed of light [tex]c= 2.99793\times10^{8}\ m/s[/tex]
Proper length of stick = 1 m
We need to calculate the length of the stick
Using formula of length
[tex]\Delta l=\Delta l_{0}\sqrt{(1-\dfrac{v^2}{c^2})}[/tex]
Put the value into the formula
[tex]\Delta l=1\sqrt{1-\dfrac{(0.96)^2c^2}{c^2}}[/tex]
[tex]\Delta l=1\sqrt{1-(0.96)^2}[/tex]
[tex]\Delta l=0.28\ m[/tex]
We need to calculate the time the stick take to move
Using formula of time
[tex]t=\dfrac{\Delta l}{v}[/tex]
Put the value into the formula
[tex]t=\dfrac{0.28}{0.96\times(2.99793\times10^{8})}[/tex]
[tex]t=9.72\times10^{-10}\ sec[/tex]
[tex]t=0.97\ ns[/tex]
Hence, The length of the stick is 0.28 m.
The time the stick take to move is 0.97 ns.
