Chapter P, Problem 27E

Relativistic Length A rocket ship travelling near the speed of light appears to a stationary observer to shorten with speed. A rocket ship with a length of $200$ meters will appear to a stationary observer to have a length of

$200\sqrt{1-r^2}$ meters,

where $r$ is the ratio of the velocity of the ship to the speed of light. What is the apparent length of the rocket ship if it is travelling at a speed that is $99\%$ of the speed of light?