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I am wondering how to solve this physics question:

-We have an object A and we have an object B

-We place these objects at a distance from each other.

-Object A has mass m.

-Object B has mass 3m.

-Object A moves toward object B with velocity v.

-Object B moves toward object A with velocity -v.

Q; What is the velocity of each object after impact?

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Can you tell me what I am doing wrong here: (I don't know where I have made a mistake)

(v1) = velocity of Object A after impact.

(v2) = velocity of Object B after impact.

Total momentum = mv-3mv= -2mv = m(v1) + 3m(v2)

Dividing both sides by m we find that:

-2v = (v1) + 3(v2)

and solving for v1 we find,

(v1) = -2v-3(v2) (1)

Using the law of conservation of kinetic energy we also get:

(.5)mv^2 + (.5)(3m)v^2 = (.5)m(v1)^2 + (.5)(3m)(v2)^2

Now divide by .5 and then by m to come up with:

4v^2 = (v1)^2 + 3(v2)^2 (2)

Inserting v1 from (1) into (2):

4v^2 = (-2v-3(v2))^2 + 3(v2)^2

4v^2 = 4v^2 + 12v(v2) + 9(v2)^2 + 3(v2)^2

-12v(v2) = 12 (v2)^2

and finally (dividing by (v2) and 12),

(v2)=-v

plugging (v2)=-v into (2) to come up with:

(v1)= v

It doesn't even make sense or look right and I have been trying to determine where I have made a mistake for days!

Thanks for any help...

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# Homework Help: Using the law of conservation of kinetic energy

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