Answer :
By using concept of conservation of momentum, we can calculate that the velocity of the launcher after the projectile is -4.9 m/s .
According to the conservation of momentum, the total momentum before launching would be same as after launching.
It means,
before launched (M1V1 + M2V2) = after launched (M1V1 + M2V2)
where, M1, V1 is the mass and velocity of launcher respectively, and
M2, V2 is the mass and velocity of the projectile object.
Now, putting the appropriate values,
4.65x2 + 0.05x2 = 4.65xV1 + 0.05x647
4.65xV1 = 9.4 - 32.35
V1 = -22.95 / 4.65
V1 = -4.9 m/s
Hence the velocity of the launcher is -4.9 m/s after the projectile is launched.
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