A ball of mass m and a ball of unknown mass M approach each other from opposite directions and have the same speed Vo (but oppositely directed velocities). The ball of M is reduced to rest by the impact, while the ball of mass m has a velocity V1'. What are the ratios(adsbygoogle = window.adsbygoogle || []).push({});

a) M / m

b) V1' / Vo

This is what I've done so far. I ended up with 2 answers, but we're only supposed to have one.

Conservation of momentum: mVo + M(-Vo) = mV1' + 0

- divide both sides by mVo, and let x = M / m, y = V1' / Vo

... equation (1'): 1 - x = y

Conservation of kinetic energy: 1/2mVo^2 + 1/2M(-Vo)^2 = 1/2mV1'^2

- divide both sides by 1/2mVo^2

... equation (2'): 1 + x = y^2

equations (1') + (2'): y^2 + y - 2 = 0

(y + 2)(y - 1) = 0

... y = -2 or 1

Case 1:

If y = -2, x = 3

Case 2:

If y = 1, x = 0

I dont know how we're supposed to determine which is the correct case. Please help!

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# Homework Help: Elastic collision - finding ratio between m2 and m1, v2 and v1

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