A particle has momentum . What is the particle’s speed in m/s?
We have given that a particle has momentum .
We have to find the particle’s speed in .
The momentum in relativity is given by
So, the equation becomes
a. Derive a velocity transformation equation for and . Assume that the reference frames are in the standard orientation with motion parallel to the x- and x′-axes.
b. A rocket passes the earth at . As it goes by, it launches a projectile at perpendicular to the direction of motion. What is the particle’s speed, as a fraction of c, in the earth’s reference frame?
The radioactive element radium (Ra) decays by a process known as alpha decay, in which the nucleus emits a helium nucleus. (These high-speed helium nuclei were named alpha particles when radioactivity was first discovered, long before the identity of the particles was established.) The reaction is , where Rn is the element radon. The accurately measured atomic masses of the three atoms are , , and . How much energy is released in each decay? (The energy released in radioactive decay is what makes nuclear waste “hot.”)
Your friend flies from Los Angeles to New York. She carries an accurate stopwatch with her to measure the flight time. You and your assistants on the ground also measure the flight time.
a. Identify the two events associated with this measurement.
b. Who, if anyone, measures the proper time?
c. Who, if anyone, measures the shorter flight time?
An astronaut travels to a star system away at a speed of Assume that the time needed to accelerate and decelerate is negligible.
a. How long does the journey take according to Mission Control on earth?
b. How long does the journey take according to the astronaut?
c. How much time elapses between the launch and the arrival of the first radio message from the astronaut saying that she has arrived?
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