Pi Measons - frame of reference

[madeeeeee]

Please help, I am confused with part c and d.

1. Doug in a lab on Earth observes a π-meson is created 2.8 km from the surface of the Earth. It has a rest decay time is 9.0 x 10-6 s and it travels straight down to the Earth at 0.95c.

a) What distance would the π-meson measure to the lab on Earth? [4]
b) To Doug in the lab on Earth, what is the decay time of the π-meson? [4]
c) In the π-meson’s frame of reference, will it make it to the Earth? Include a calculation. [2]
d) In the Earth frame of reference, will the π-meson make it to the surface? Include a calculation.

Answer:
a) the distance calculated is 874 m
b) time calculated is 2.88 x 10^-5 s
c) I don't know what this means - can someone please explain pi measons and there frame of reference to Earth
d) i don't know what this is asking

thank you :)

 

[vela]

When the pi meson decays, it turns into other particles. The question is asking you if the meson is likely to reach the surface of the Earth intact or if it will decay in transit instead.

In the frame of the pi meson, it's at rest, so it'll decay on average in $9.0\times10^{-6}~\textrm{s}$. It sees the surface of the Earth starting at 874 meters away and moving toward it 0.95c. So the question is asking you if the surface of the Earth will reach the meson before it's likely to decay.

Similarly, in Doug's frame, you see the meson traveling down toward the Earth. If it doesn't survive long enough, it will decay in transit and never reach the surface.

Obviously, you should find the same answer in both frames. It either reaches the surface or it doesn't. You need to show calculations for each frame to support your conclusion.