Show that the ratio of velocities of equal masses in an inelastic collision when one of the masses is stationary is 1 2 = 1− 1+ .
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Answer:
In a perfect elastic collision
v
1
=
m
1
+m
2
u
1
(m
1
−m
2
)+2m
2
u
2
v
2
=
m
1
+m
2
u
2
(m
2
−m
1
)+2m
1
u
1
Given that u
2
=0 and v
1
=−v
2
(since, they are in opposite direction)
v
1
=−v
2
⇒
m
1
+m
2
u
1
(m
1
−m
2
)
=−
m
1
+m
2
2m
1
u
1
⇒u
1
(m
1
−m
2
)=−2m
1
u
1
⇒m
1
−m
2
=−2m
1
⇒3m
1
=m
2
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