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## Cosmic Rays: Instructor's Guide

### Main Ideas

1. Understanding time dilation and length contraction.
2. Using spacetime diagrams to solve problems.

Estimated Time: 45 minutes, including wrap-up

Groups are asked to analyze the following standard problem:

##### Cosmic Rays

Consider mu-mesons produced by the collision of cosmic rays with gas nuclei in the atmosphere 60 kilometers above the surface of the earth, which then move vertically downward at nearly the speed of light. The halflife before mu-mesons decay into other particles is 1.5 microseconds.

Assume all the mesons are traveling straight down at the same speed.

1. Assuming it doesn't decay, how long would it take a mu-meson to reach the surface of the earth?
2. Assuming there were no time dilation, approximately what fraction of the mesons would reach the earth without decaying?
3. In actual fact, roughly 1/8 of the mesons reach the earth! How fast are they going?

### Prerequisite Knowledge

• basic understanding of time dilation
• basic understanding of spacetime diagrams

### Wrap-Up

• Have students present and compare their solutions.

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