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# Problems in Modern Physics

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Problem 1. Bob is watching Anna ï¬‚y by in her high-speed plane, which Anna knows
to be 70 m in length. As a greeting, Anna turns on two lights simultaneously, one in front
and one at the tail. According to Bob, the lights come on at different times, 45 ns apart.
How fast is the plane moving?

Problem 2. A muon has a mean lifetime 2.2 ps in its rest frame. Suppose muons are
traveling at 0.930 relative to Earth.
What is the mean distance a muon will travel as measured by an observer on Earth?

Problem 3. An electron accelerated from rest through a potential difference V acquires
a speed of O.9995c.
Find the value of V.

Problem 4. An object of mass mo heading east at 0.80 collides with an object of mass
gmo moving west at 0.6c. After collision the two stick together.
Find the mass my and speed u ; of the resulting combined object.

Problem 5. A star during its evolution has the surface temperature decreased from
200,000K to 120,000K.
a). What are the wavelengths of maximum intensity produced at each temperature?
b). By what factor does the the total power radiated per unit area change?