YouTube Lecture # 84

1. 1
The proper lifetime of a certain particle is 100.0 ns.
(a)How long does it live in the laboratory if it moves at
v = 0.960c?
(b) How far does it travel in the laboratory during that time?
(c) What is the distance traveled in the laboratory according
to an observer moving with the particle?

2. 2
Helping Tools
No.1

3. 3
No.2
Solution

4. 4
(a)
0
2
2
9 7
0
7 7 7
2 2
2
7 7
7 9
(1)
1
,
100.0 100 10 10 , 0.960
Putting in (1), we get
10 10 10
1 0.9216
(0.960 ) 1 (0.960)
1
10 10
3.571 10 357.1 10 357.1
0.28
0.0784
t
t
u
c
Here
t ns X s s u c
s s s
t
c
c
s s
X s X s ns
− −
− − −
− −
− −

 = − − − − − − − − − − − −
−
 = = = =
 = = =
−
−
−
= = = = =

5. 5
(b)
9
8 9
1
(0.960 ) X357.1X10
0.960 2.998 10 357.1 10
1027.76 10 102.776
d v t c s
m
X X X X s
s
X m m
−
−
−
=  =
=
= =

6. 6
(c)
0 0
8 9
0.960 100.0
0.960 2.998 10 100.0 10
2.87808 10 28.7808
d v t cX ns
m
X X X X s
s
X m m
−
=  =
=
= =
The End