In an elastic collision, an object with momentum 12 kg·m/s collides with another. the final momenta of each are 14 kg∙m/s and 16 kg∙m/s respectively. what was the initial momentum of the second object

We know that in an elastic collision the moments of the both the objects is conserved i. e

Intial momentum of object1 + Intial momentum of object2 = Final momentum of object1 + Final momentum of object2

Intial momentum of object1 = 12 kg. m/s

Intial momentum of object2 = P (assume that P is the momentum)

Final momentum of object1 = 14 kg. m/s

Final momentum of object2 = 16 kg. m/s

On substituting all values we get

12 + P = 14 kg. m/s + 16 kg. m/s

P = - 18 kg. m/s

(-ve sign indicates the second object was moving in the opposite direction to the object1 before collision)

Therefore the initial momentum of the second object was 18 kg. m/s.