Relativity question involving time dilation

[MiniOreo1998]

Homework Statement

A muon has a lifetime of 2.20 x 10⁶ 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 0.99 c, 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 Earth's reference frame or referenced who viewed the muon moving at 0.99 c?

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

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

I'm unsure of B and C. Any help would be appreciated!

Homework Equations

Δt_m = Δt_s / √ 1 - v² / c²

The Attempt at a Solution

A)
0.99 (3 x 10⁸ = 2.97 x 10 ⁸
2.97 x 10 ⁸ (2.20 x 10 ^-6 = 653.4

B)
Δt_m = Δt_s / √ 1 - v² / c²
Δt_m = 2.20 x 10^-6 / 1 - 0.99 (3.0 x 10⁸)²
Δt_m = 9.8 x 10^-6

C)
0.99 (3 x10⁸ (9.8 x 10^-6= 2910.6 m

D) As the particle approaches the speed of light time dilation becomes more prevalent, causing the muon to last longer

 

[Orodruin]

Δtm = Δts / √ 1 - v2 / c2
Δtm = 2.20 x 10-6 / 1 - 0.99 (3.0 x 108)2

Your math is off. It is also impossible to tell exactly what you are doing because you are not writing out parentheses and units properly. Parentheses are important in order for your expressions to be readable to anyone, including yourself. Physical quantities always has units. You cannot say that Δt = 2.2 without specifying which units you are using.