The velocity of .5 kg ice puck before collision = u1= 3.30 m/s
The velocity of .9 kg ice puck before collision = u2= 0
The velocity of .5 kg ice puck after collision = v1=?
The velocity of .9 kg ice puck after collision = v2=?
According to conservation of momentum,
m1u1 + m2u2 = m1v1 + m2v2
=> (u1-v1)m1 = (v2-u2)m2 ....(i)
Again, conservation of energy gives
1/2 m1u1^2+ 1/2 m2u2^2 = 1/2 m1v1^2 + 1/2 m2v2^2
=> m1(u1^2 - v1^2) = m2(v2^2 - u2^2) .....(ii)
Divide (ii) by (i)
(u1^2 - v1^2)/(u1-v1) = (v2^2 - u2^2)/(v2-u2)
=> u1+v1 = v2+u2
=> v1= u2+v2-u1 = v2-u1 ....(iii). [u2=0]
Now, substitute v1 in (i)
(u1-v2+u1)m1 = (v2-u2)m2
=> 2m1u1 - m1v2 = m2v2
=> (m1+m2)v2 = 2m1u1
=> v2 = (2m1u1)/(m1+m2) ....(iv)
Substitute v2 in (iii)
v1= v2-u1 = (2m1u1)/(m1+m2) -u1
=> v1 = (2*.5*3.30)/(.5+.9) - 3.30 = 2.357 - 3.30 = -0.943 m/s
(-) sign indicates that the ice puck is moving to the west.
Now substitute v1 in (iii) again
v1 = v2-u1
=> v2 = u1+v1 = 3.30 - 0.943 = 2.36 m/s
It means it is going to the east.
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