A meterstick is shot from a meterstick projector at a speed of 0.90c. How long will it be relative to an observer's frame of reference?
A)2.3 m
B)0.91 m
C)1.0 m
D)0.44 m
E)0.81 m

Question

Quizplus · Accepted Answer

According to the length contraction formula, the length of the meterstick will be L' = L/γ, where L is the rest length of the meterstick (1 meter) and γ is the Lorentz factor, given by γ = 1/√(1 - v^2/c^2). Plugging in the given values, we get γ = 1/√(1 - 0.9^2) ≈ 2.94. Therefore, L' = 1/2.94 ≈ 0.34 meters. However, the question asks for the length relative to an observer's frame of reference, which means we don't need to take into account any direction of motion. Hence, we need to double this value to get the final answer: L' = 2 × 0.34 ≈ 0.68 meters, which is closest to answer choice D (0.44 m is too small, 0.81 m is too large, and 1.0 m and 2.3 m are not even close).

A Meterstick Is Shot from a Meterstick Projector at a Speed