With what speed should an object move so that its longitudinal length in a state of motion

With what speed should an object move so that its longitudinal length in a state of motion is three times less than its rest length?

Dependence of the size of the body L on the speed v (the size changes, which coincides with the direction of the speed):

L = L0 * √ (1 – v ^ 2 / c ^ 2),

where L is the size of the body in motion, L0 is the size of the body at rest, c is the speed of light in vacuum.

By hypothesis, L = L0 / 3.

L0 / 3 = L0 * √ (1 – v ^ 2 / c ^ 2);

1/3 = √ (1 – v ^ 2 / c ^ 2);

1/9 = 1 – v ^ 2 / c ^ 2;

v ^ 2 / c ^ 2 = 8/9

v / c = (2√2) / 3;

v = (2c√2) / 3 ≈ (2 * 10 ^ 8 m / s * 1.414) / 3 ≈ 9.4 * 10 ^ 7 m / s.

Answer. Velocity v = (2c√2) / 3 ≈ 9.4 * 10 ^ 7 m / s.