Environmental Engineering Reference
In-Depth Information
two events as measured in frame
S
moving with constant velocity parallel
to the
x
-axis and in which their spatial separation is measured to be 2 km?
6.14 In a particular inertial frame, two pulses of light are emitted at a distance
4 km apart and are separated by 5
s in time. An observer travelling at speed
v
along the line joining the emission points of the two pulses notes that the
pulses are emitted simultaneously. Find
v
.
6.15 In 1994, a rather eccentric group of astronomy students wanted to celebrate
the impact of the Shoemaker-Levy comet on Jupiter by holding a party of
sufficiently long duration that their celebrations were simultaneous with the
impact of the comet in all possible inertial frames. For how long did they
need to party? How might the party end?
[The distance from the Earth to Jupiter is 8
µ
10
11
m and you may neglect
×
their relative motion.]
6.16 Two particles are created in a particle physics experiment. They move apart
in opposite directions, with one particle travelling at a speed of 0
.
70
c
and the
other at a speed of 0
.
850
c
as measured in the laboratory. What is the speed
of one particle relative to the other? Compare your answer to that which you
would expect using classical ideas.
6.17 A rocket moves away from the Earth at a speed of 0
.
5
c
and at a later time
sends out a second rocket which travels back towards the Earth at a speed
of 0
.
8
c
relative to the parent rocket. What is the speed of the second rocket
relative to the Earth?
6.18 The passage of light through a medium is characterised by a refractive index
n
and the velocity of light relative to the medium is
c/n
. Suppose that such
a medium is moving with speed
v
parallel to the direction of propagation
of the light. Derive an expression for the speed of light,
V
, as observed by
a stationary observer. Show that your result can be used to explain Fizeau's
experimental findings of 1851 which used light passing through flowing water
to demonstrate that
v
1
n
2
.
c
n
+
1
V
≈
−
6.19 Two rockets, A and B, start from a common point C and travel with constant
speeds
u
in directions perpendicular to each other as observed in the rest
frame of C. An observer in A measures the angle BAC to be 30
◦
.Whatis
the value of
u/c
?
