Question

Relative to the frame of the observer making the measurement, at what speed parallel to its length is the length of a meterstick 60 cm?

Answer 1

The speed of the observer is 2.4 x 10^8 m/s

Step-by-step 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

`l = l_(0)\sqrt{1 - \beta ^(2) }`

where

`l` is the new length of 60 cm

`l_(0)` is the original length which is 100 cm

`\beta` 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 =
`100\sqrt{1 - \beta ^(2) }`

0.6 =
`\sqrt{1 - \beta ^(2) }`

we square both side

0.36 = 1 -
`\beta ^(2)`

`\beta ^(2)` = 1 - 0.36 = 0.64

β =
`√(0.64)` = 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