Question

A 2kg ball moving at 6 ms collides head on
with a 3kg ball moving in the opposite
direction at12 m/s. The velocity of each ball
after the impact, if the coefficient of
restitution is 1/2, is
(A) -10.2m/s; – 1.2 m/s
(B) –10 m/s; – 2 m/s
(C) 10 m/s; 14 m/s
(D) 10.2m/s, - 2 m/s​

Answer 1

Answer:

Let initial velocities of 1kg ball and 2kg ball be u

1

,u

2

respectively and final velocities be v

1

,v

2

respectively .

By conservation of linear momentum ,

1×u

1

+2×u

2

=1×v

1

+2×v

2

u

1

=12m/s,u

2

=−14m/s

v

1

+2v

2

=−16

Coefficient of restitution e=

3

2

e=

u

2

−u

1

v

2

−v

1

=

3

2

3v

1

−3v

2

=52

Solving these equations,

v

1

=

9

56

,v

2

=−

9

100

Loss of kinetic energy

δK=

2

1

[u

1

2

+2u

2

2

−v

1

2

−2v

2

2

]=125J

Option B is closest.

Explanation:

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