Question

In this example we will see that time dilation is a rather small effect for reference frames in which u≪c. An airplane flies from San Francisco to New York (about 4800 km, or 4.80×106m) at a steady speed of 300 m/s (about 670 mi/h) (Figure 1). How much time does the trip take, as measured (a) by observers on the ground and (b) by an observer inside the plane?The π+ meson (or positive pion) is an unstable particle that has a lifetime (measured in its rest frame) of about 2.60×10−8s. If the particle is moving with a speed of 0.992 c with respect to your laboratory, what is its lifetime as measured in the laboratory?

Answer 1

2.) For the +ve pion particle, Using time dilation,

It's lifetime as measured in the laboratory

T = T_o/1 - (v/c)²

= 2.60*10^-8/1 - 0.992²

= 2.06*10^-7 s.

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