Where is V f2 =(2m 1 /m 1 +m 2 )V 01 come from?? My instructor keep doing with V

Question

Where is Vf2=(2m1/m1+m2)V01 come from?? My instructor keep doing with Vf2=(m1/m2)(V01-Vf1) What's the difference. becasue sometimes top one is right and sometimes bottome one is right. Where is Vf2=(2m1/m1+m2)V01 come from?? My instructor keep doing with Vf2=(m1/m2)(V01-Vf1) What's the difference. becasue sometimes top one is right and sometimes bottome one is right. come from?? My instructor keep doing with Vf2=(m1/m2)(V01-Vf1) What's the difference. becasue sometimes top one is right and sometimes bottome one is right.

Explanation / Answer

when elastic collision takes place in one dimesnion between twobodies of masses m1 and m2 having initil velocities as u1 , u2 andv1 , v2 as the final velocities after collision. then we have, u1 - u2 = v2 - v1 and also, v 1 = ((m1-m2)/ (m1+ m2))u1 + ( 2m2/ ( m1+ m2)) u2 so now in this case if m1= m2 then we have v 1 = 2m1/(m1+ m2) u2 which is your first case so it is taken into use when bothe themasses are equal similarlu u can judge very easily for the other formula

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