Special Relativity and Decaying Particles

[Rapier]

Homework Statement

Pions are part of a class of short-lived particles called mesons which commonly created during the collisions in scientific accelerators or when cosmic rays collide with particles in the upper part of the Earth's atmosphere. A type of pion known as a π+ has a mass of 139.6 MeV/c2. One particular π+ was created during a collision in the Earth's upper atmosphere and has an total energy E= 1.25 X 105 MeV. As measured in its own frame, it has a life time of 38 nsec before it decays.
a) If it decays at a point 146 meters above sea-level, how high above sea-level was the comsic-ray collision that created the pion?

hcollision = m
255345.052163 NO

HELP: Provide this information in the frame of reference of an observer on earth.
HELP: How are the total energy and mass of an object related?

b) How long does the particle live in the frame of reference of an observer on earth??
Δtearth = nsec

c) In the frame of reference of the pion, how far does it traveled before it decayed?
Δxπ = m *
11.39 OK

Homework Equations

d ' = dγ
γ = sqrt (1 - v^2/c^2)
E = K - mc^2
K = mc^2[(1/γ)-1]

The Attempt at a Solution

I used total energy + rest energy (E + mc^2) = kinetic energy (K). When I solved K for V I found that the particle was moving nearly at the speed of light. .999999999004c (that's 9 9s).

I used that speed to calculate my γ = 4.46318e-5.

d' = dγ
11.39m = d (4.46318e-5)
d = 255199.052163 m

The particle decayed 146m about sea level so d+146 = 255345.052163.

But it tells me no, so I believe the error might have come in calculating my V. If I can get A, B will be no problem...but I'm stuck.

Help! Thanks!

 

[vela]

You have a sign error in one of your equations. The total energy is the sum of the rest energy and the kinetic energy.

Your value for $\gamma$ can't possibly be correct since $\gamma \ge 1$.

 

[Rapier]

You have a sign error in one of your equations. The total energy is the sum of the rest energy and the kinetic energy.

Your value for $\gamma$ can't possibly be correct since $\gamma \ge 1$.

I corrected my sign error: E = k + mc^2. However, that doesn't really change anything. My energy is 1.25e5 and the 139.6 MeV of mass isn't making any appreciable change in my kinetic energy. I'm getting the same answer.

 

[vela]

What are you getting for $\gamma$? You should get $\gamma=895$.