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Chapter 22: Problem 35

How fast should a meter stick be moving in order to appear to be only \(60 \mathrm{~cm}\) long?

Short Answer

Expert verified
The meter stick should be moving at a speed of \(0.8c\) in order to appear to be only 60 cm long.

Step by step solution

01

Formulate the equation

The equation based on the length contraction formula would be: \(60 = 100 \sqrt{1 - \frac{v^2}{c^2}}\)
02

Rearrange the equation to isolate the variable under the square root

First, divide both sides by 100, which gives: \(0.6 = \sqrt{1 - \frac{v^2}{c^2}}\). Then square both sides to get rid of the square root, which gives: \(0.36 = 1 - \frac{v^2}{c^2}\)
03

Solve for \(v^2\)

Rearrange the equation to get \(v^2\) alone on one side, which gives: \(v^2 = (1 - 0.36) \cdot c^2 = 0.64 \cdot c^2\)
04

Calculate the velocity

Finally, take the square root of both sides to solve for \(v\), and obtaining the velocity in terms of \(c\), which is: \(v = \sqrt{0.64} \cdot c = 0.8c\)

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