How fast must a meter stick move relative to an observer so

How fast must a meter stick move relative to an observer so that she would measure its length to be 8.0 cm? (Enter your answer to five significant figures.)

Solution

given that

L0 = 8 cm = 0.08 m

L = 1 m

formula for lorentz transform

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

L^2/L0^2 = 1-v^2/c^2

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

v/c = sqrt(1-0.08^2/1)

v/c = 0.996

v = 0.996*c = 0.996*3*10^8

v = 2.99*10^8 m/s