A particle in a 799=m-long linear particle accelerator is moving at $0.875 c$ How long does the particle accelerator appear to the particle?
A) 387 m
B) 1039 m
C) 184 m
D) 1651 m

Question

Quizplus · Accepted Answer

We can use the formula for length contraction:
$L_{s}=L_{o}\sqrt{1-\frac{v^{2}}{c^{2}}}$
where $L_{s}$ is the contracted length, $L_{o}$ is the rest length, $v$ is the velocity of the object, and $c$ is the speed of light.
Plugging in the values, we get:
$L_{s}=799\sqrt{1-(0.875)^{2}}=387$ m
Therefore, the particle accelerator appears to be 387 m long to the particle.

A Particle in a 799=m-Long Linear Particle Accelerator Is Moving 0.875c0.875 c0.875c

A Particle in a 799=m-Long Linear Particle Accelerator Is Moving $0.875 c$