Special Relativity

Relativistic Range of a Muon:

A muon has a lifetime of 2×106s in its rest frame. It is created in the upper atmosphere and moves towards Earth at a speed of 0.99c. From the point of view of an observer on Earth, how far does the muon travel before it decays?

Relativistic Addition of Velocities:

Two alien spaceships approach each other, each moving with the same speed as measured by a stationary observer on the Earth. Their relative speed, as measured by the aliens, is 0.8c. Determine the speed of the spaceships as measured by a stationary observer on Earth.

Determining if events are causally connected:

Three events, A, B and C are measured in the same inertial frame. Their 2-D space-time (y=z=0) coordinates are: A (x = 4m, t = 10-8s), B (x = 1m, t = 10-8s) and C (x = 6m, t = 2×10-8s). Determine which, if any, of these events are causally connected.


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