Sanity Check- Momentum/Collision Question

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I would appreciate a sanity check as my solution just doesn't "feel" right.

The question: A very small object with a mass of m and velocity of +2v catches up to and strikes a much larger object in motion with a velocity of +v and a mass of M, in a perfectly elastic, head-on, one-dimensional collision.

We know from that momentum and Kinetic energy are conserved.

Thus,

v₁ + v₁' = v₂'+v₂

Which when stated means: the relative speed between the two particles before and after the collision is equal. Regardless, of the masses.

Approximating the speed of the large object to be equal before and after the collision

v₂ ≃ v₂'

By substitution

2v + v₁' = v + v

=> v₁' = 0

Thus, the small mass is at rest after the collision.

Which again, just "feels" wrong, but looks right, Math-wise.

Thoughts?

Ciaran

I right I wrote: »

Approximating the speed of the large object to be equal before and after the collision

v₂ ≃ v₂'

This is your problem. The speed of the large mass before and after isn't equal. It mightn't change much but the small change for the large mass will cause a larger change for the small mass.