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?

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

where

is the new length of 60 cm

is the original length which is 100 cm

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 =

0.6 =

we square both side

0.36 = 1 -

= 1 - 0.36 = 0.64

β = = 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