Say that the mean lifetime of a π+ meson in its own rest frame is τ = 2.6 x 10-8 s. A pion of this lifetime is created at an altitude 100 km in the atmosphere by the collision of an incoming cosmic·ray proton with an atmospheric nucleus, and it has lifetime τ. How fast would this π+ meson need to move in order to reach the ground before decaying? Express the velocity in the form v/c = 1 - ϵ, where ϵ << 1. (Hint: Use the binomial approximation.)
Say that the mean lifetime of a π+ meson in its own rest frame is τ = 2.6 x 10-8 s. A pion of this lifetime is created at an altitude 100 km in the atmosphere by the collision of an incoming cosmic·ray proton with an atmospheric nucleus, and it has lifetime τ. How fast would this π+ meson need to move in order to reach the ground before decaying? Express the velocity in the form v/c = 1 - ϵ, where ϵ << 1. (Hint: Use the binomial approximation.)
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Say that the mean lifetime of a π+ meson in its own rest frame is τ = 2.6 x 10-8 s. A pion of this lifetime is created at an altitude 100 km in the atmosphere by the collision of an incoming cosmic·ray proton with an atmospheric nucleus, and it has lifetime τ.
How fast would this π+ meson need to move in order to reach the ground before decaying? Express the velocity in the form v/c = 1 - ϵ, where ϵ << 1. (Hint: Use the binomial approximation.)
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The object's velocity provides a good indication of its position as well as its rapidity. Objects can be measured by the distance they cover in a unit of time.The velocity of an object can be defined as its displacement in a unit of time.
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