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Jack and Annie are standing facing each other on frictionless ice at position x=0. They give...

Jack and Annie are standing facing each other on frictionless ice at position x=0. They give each other a sharp push, so that after they have contact Jack is moving in the negative x direction with a speed of 5 m/s. Jack has a mass of 60kg and Annie has a mass of 40kg. What is the position of their center of mass after 4 seconds?
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Answer #1

let the speed of annie after pushing be v m/s

By the conservation of momentum

m1u1 = m2u2

60*5 = 40*v

v = 7.5 m/s

position of jamie after 4 s = -5*4 = -20 m

position of annie after 4s = 7.5*4 = 30 m

position of centre of mass = m1x1 + m2x2 / m1 + m2

= 60*-20 + 40*30 / ( 60 + 40)

= 0

so the position of COM after 4s is x =0

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