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we are given
for ball 1
m1 = 1 kg
u1 = 12 m/s
and
for ball 2
m2 = 2 kg
u2 = 24 m/s
now,
the coefficient of restitution is given as
e = (v2 - v1) / (u1 - u2) = 2/3 = 0.66
so,
(v2 - v1) = 0.66 x (u1 - u2) = 0.66 x (12 - 24)
or
(v2 - v1) = -7.92
v2 = v1 - 7.92 ..............................(1)
now, as e
m1u1 + m2u2 = m1v1 + m2v2
1x12 + 2x24 = 1xv1 + 2xv2
60 = v1 + 2v2
v2 = (60 - v1) / 2 ...........................(2)
by equating (1) and (2), we get
v1 - 7.92 = (60 - v1) / 2
or by rearranging
2v1 + v1 = 60 + 2x7.92
3 v1 = 75.48
thus,
v1 = 25.16 m/s
v2 = 25.16 - 7.92 = 17.24 m/s
loss in kinetic energy will be
dE = Ei - Ef = [(1/2)m1u12 +(1/2)m2u22] - [(1/2)m1v12 +(1/2)m1v22]
which can be calculated...
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