Question

A meter stick moves parallel to its axis with speed of 0.96 c relative to you. What would you measure for the length of the stick? The speed of light is 2.99793 × 108 m/s. Hong does it take for the stick to move past you?

Answer 1

The length of the stick is 0.28 m.

The time the stick take to move is 0.97 ns.

Step-by-step explanation:

Given that,

Relative speed of stick v= 0.96 c

Speed of light
`c= 2.99793*10^(8)\ m/s`

Proper length of stick = 1 m

We need to calculate the length of the stick

Using formula of length

`\Delta l=\Delta l_(0)\sqrt{(1-(v^2)/(c^2))}`

Put the value into the formula

`\Delta l=1\sqrt{1-((0.96)^2c^2)/(c^2)}`

`\Delta l=1√(1-(0.96)^2)`

`\Delta l=0.28\ m`

We need to calculate the time the stick take to move

Using formula of time

`t=(\Delta l)/(v)`

Put the value into the formula

`t=(0.28)/(0.96*(2.99793*10^(8)))`

`t=9.72*10^(-10)\ sec`

`t=0.97\ ns`

Hence, The length of the stick is 0.28 m.

The time the stick take to move is 0.97 ns.