Trouble answering this please review

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The forum discussion centers on solving a physics problem involving elastic collisions between two objects with masses of 18g and 33g, moving at velocities of 26cm/s and 16cm/s, respectively. The user attempts to apply the conservation of momentum and kinetic energy equations but arrives at incorrect final velocities for both objects. The correct approach involves using the kinetic energy formula, K.E. = 1/2 mv², to derive the final velocities accurately by substituting one equation into the other.

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Ive been working this problem for the past hours, and i keep getting the wrong answer... can someone check to see what I am doing wrong, and please correct me..

Question:
An 18g object moving to the right at 26cm/s overtakes and collides elastically with a 33g object moving in the same direction at 16cm/s.

I need to find the velocity of the slower object and then the faster object.

My attempt at this question:
m1v1 + m2v2 = m1v1f + m2v2f
(.018)(26) + (.033)(16) = (.018)v1f + (.033)v2f
(.468) + (.528) = (.018)v1f + (.033)v2f
(.996)= (.018)v1f + (.033)v2f

then KE cons.
26-16 = -(v1f-v2f)
10=v1f + v2f
v1f = -10 + v2f

and subsituted (v1f = -10 + v2f) in v1f in the first eq.

(.996)= (.018)(-10 + v2f) + (.033)v2f
(.996)= (-.180) + (.018)v2f + (.033)v2f
(.996)= (-.180) + (.051)v2f
(1.176)= (.051)v2f
(1.176/.051) = v2f
v2f= 23.05882 (((<<< this is for the slower object)))

For the faster object I work the problem the same way, only using the substitution for v2f this time.

And Its incorrect. please help!
 
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You're trying to take a shortcut for the K.E.

Use : K.E. = \frac{1}{2}mv^{2}

Then get v_{1f} and v_{2f} using that and you've already got it for the first equation, so plug one of the found velocities into the other equation and it should work out.

*gulps* I sure hope I'm not messing this up. I should really check before posting; but I'm sure someone will correct me if I'm wrong.