Question

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+ .

Answer 1

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