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## Homework Statement

**A muon has a lifetime of 2.20 x10-6 s when at rest, after which time it decays into other particles.**

**a) Ignore any effects of relativity discussed in this section. If the muon was moving at 0.99c, how far would it travel before decaying into other particles, according to**

__Newtonian mechanics__?**b) How long would the muon last, according to an observer in the earth’s frame of reference who viewed the muon moving at 0.99c?**

**c) How far would the muon actually travel, when viewed moving at 0.99c?**

**d) Compare the two distances travelled. Explain why this type of evidence is excellent support for the theory of relativity.**

## Homework Equations

Δt

_{m}= Δt

_{s}/

**√1- v**

^{2}/c^{2}## The Attempt at a Solution

a) With Newtonian mechanics, there would be no time dilation so:

0.99c(3.00x10

^{8})

= 2.97 x10

^{8}m/s

(2.97 x10

^{8}m/s) (2.20 x10-6 s)

= 653.4m

According to Newtonian mechanics, the muon would travel 653.4m.

b)

Δt

_{m}= Δt

_{s}/ √1- v

^{2}/c

^{2}

Δt

_{m}= 2.2 x10

^{-6}/ √1- 0.99c

^{2}/c

^{2}

Δt

_{m}= 2.2 x10

^{-6}/ √1 - 0.9801

Δt

_{m}= 1.56 x10

^{-5}s

According to an observer on earth, the muon will last for 1.56 x10

^{-5}s.

**I am not sure how to calculate distance with respect to relativity, we've only learned equations for time dilation, mass and length contraction. Is there a specific formula for distance that I don't know about?**

c)

c)

Also, I tried to calculate a with Newtonian mechanics but I'm not completely sure if that is what the question is asking for.

Any help on this is greatly appreciated, I know I must be missing something but just can't think of it; this question has been driving me crazy!