A particle lives for a short time before breaking apart into otherparticles. Sup

Question

A particle lives for a short time before breaking apart into otherparticles. Suppose it is moving at a speed of 0.984c, and an observer who is stationary ina laboratory measures the particle's lifetime to be 3.00 x 10-8 s. (a) What is the lifetime according to ahypothetical person who is riding along with theparticle? s

(b) According to this hypothetical person, how far does thelaboratory move before the particle breaks apart?
m

(a) What is the lifetime according to ahypothetical person who is riding along with theparticle? s

(b) According to this hypothetical person, how far does thelaboratory move before the particle breaks apart?
m

Explanation / Answer

Given :

A particle lives for a short time beforebreakingapart into other particles. Suppose it is movingat a speedof 0.984c , where c is the speed of light,and an observer who isstationary in a laboratorymeasures the particle's lifetime to be3.0*10-8 s

(a)

Lifetime, Hypothetical Person Frame ( T) =
          ( T )= Lab Frame Lifetime*[1 - (v/c)2] =
          = (3.0*10-8)*( 1 - (0.984)2)
         =  5.3*10-9 sec

(b)
Distance  = (Lifetime, Hyp Person Frame)*(Velocity)
                  =( T ) * v                    = (5.3*10-9)*((0.984)*(3*108))
                  = ----- meter Solve it I hope it helps you

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