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Problems on the Postulates and Simultaneity
Problem 1.1:
Someone on a moving train on the earth measures the speed of a meteor in
space to be 5×106 m/s. Someone in outer space measures the
speed to be 4×106 m/s. Who is right?
[Solution]
Problem 1.2:
Two spaceships are hurtling towards one another at a constant speed of
0.8c. When they are still 10 000 kilometers apart, one spaceship radios
the other to warn them of the impending collision. How much time does it
take for the radio wave to reach the other ship, as observed by someone on
the receiving ship (assume that the spaceships move little in the time
taken for the signal to travel between them)?
[Solution]
Problem 1.3:
Consider the situation described in Section 1. If the flashes
from the sources are observed to occur simultaneously by an observer
standing on the ground (at rest relative to the sources), what is the time
difference between the events according to an observer on a train speeding
past at 0.15c, if that observer measures the distance between the
sources to be 1 kilometer?
[Solution]
Problem 1.4:
What if the scenario described in Section 1 is performed with
baseballs (which travel at a constant speed b < c) instead of light
pulses. Will the observers still disagree?
[Solution]
Problem 1.5:
Consider again the scenario described in Section 1. Now
consider changing the setup by placing only a single emitter at the center
position (where OA was), and having two receivers placed where the
sources formerly were. The source emits two signals, one in each
direction (that is, one towards each receiver). An observer at rest with
respect to the source and receivers concludes that the source emitted its
two signals simultaneously. What does an observer traveling to the right
at velocity v observe?
[Solution]
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