The 500 m-long spaceship Springbrake is at rest on the planet Hitest for refueling. Another spaceship, Summerbrake, passes parallel to Springbrake at 0.600c. The crew on Springbrake measure the length of Summerbrake as it passes and find that the length they measure is exactly the same as the known 500 m rest length of Springbrake. If Summerbrake were at rest next to Springbrake, its length would then be measured to be
A) 180 m.
B) 320 m.
C) 500 m.
D) 625 m.
E) 781 m.

Question

Quizplus · Accepted Answer

The length contraction formula is $L = L_0\sqrt{1 - v^2/c^2}$, where $L$ is the observed length, $L_0$ is the rest length, and $v$ is the velocity of the object. Given that the observed length $L$ is 500 m and $v = 0.600c$, we can solve for $L_0$. Rearranging the formula to solve for $L_0$, we get $L_0 = L / \sqrt{1 - v^2/c^2}$. Plugging in the values, $L_0 = 500 / \sqrt{1 - 0.600^2}$, which calculates to approximately 625 m. This means that when Summerbrake is not moving, its rest length would be measured as 625 m.

The 500 M-Long Spaceship Springbrake Is at Rest on the Planet