o +u'
L
=
;
=
l+au'/c'
0.90c
+ 0.70c
 + (o.9oc)
(0.70c)f
cz
Homework 2 Solutions
=
0.98c
LM
t?3
(b)
(c)
(a)
729
(a)
[,et event t have coordinates.rt
=y1 =a =tl =0
and event 2 have coordinates
x2=100
as1, y"= 22=
tz
=0.kr
S'
,
xi=7@rvtr)=0, yi
=y, =Q,
7i
=7, =Q,a1Q

/a\
f
,,2fv2
,i
=
4,,
l#),,
l=
o, wtth
/
Lr

+j
""a
*
r
=[r
1s.7o121vz
1.40.
In
system
S', x'2
y$tatr)=740 m, yi =
zi
=O,
and
t
r[ t"
(
a\'"1
(l
4x{ 70X100
m)
{.33 ,,s
.
'
'L'
\c' )
'J
3.mxl0' ry's
M'
x'z xi
=l4o
m
Events are not simultaneous in S', event 2 occurs 0.33
/s
earlier than event 1.
A spaceship,
referenct frame S', moves at speed o relative to the Earft, whose
reference
frame is 5. The space ship then launches a shutde craft with velocity o in
the forward direction. The pilot of the shutde craft then fires a probe with velocity a
in the forward direction. Use the relativistic compounding of velocities as rvell as
its
inverse
rrarrsfomn
tio".
":,
=
ffifl,
and
its
inverse
u,
=
ffi4.m"
uA""u
variables are defined as: o is the spaceship's
velocity relative to S, z! is the velocity of
the shutde craft reLative
to S', and r, is the velocity of the shuttle craft relative to S.