Question

27.11 A meter stick moves past you at great speed.Its motion relative to you is parallel to its long axis. If you measure the length of the moving meter stick to be 1.90ft for example, by comparing it with a ruler that is at rest relative to you, at what speed is the meter stick moving relative to you?

Answer 1

here,

length of meter stick at rest , L0 = 1 m

lenth of meter stick as seen by us , L = 1.9 ft (1ft=0.3048m)

L = 0.57912 m

let the velocity of meter stick be v

L = L0 sqrt(1 - (v/c)^2)

0.57912 = sqrt(1-(v/c^2))

v = 0.815c

v=2.445*10^8 m/s