A block of mass m undergoes a one dimensional elastic collision with a block of

Question

A block of mass m undergoes a one dimensional elastic collision with a block of mass M initially at rest. If both blocks have the same speed after colliding how are there mass related?

I know that
m1=m mass of first block
m2=M mass of second block
vu=u1 initial speed of first block
v1f=v1 final speed of first block
v2i=u2 initial speed of second block
v2f=v2 final speed of second block

v1=( m1+m2/m1+m2) u1 + (2m2/m1+m2) u2

v2= (m2-m1/m1+m2) u2 + (2m1/m1+m2) u1

(m1-m2/m1+m2) u1 + (2m2/m1+m2) u2

(m2-m1/m1+m2) u2 + (2m1/m1+m2) u1


M2=-m1

m=-M

Express M in terms of m I solved the problem but I don't know the final answer

my answers were
-1m and it is saying that it is wrong
this is the message it is giving me
Your answer either contains an incorrect numerical multiplier or is missing one.

please help

Explanation / Answer

by applying conservation of momentum

mu1 + Mu2 = (M + m)v1

mu1 = (m + M)v1

now

v1=( m1+m2/m1+m2) u1 + (2m2/m1+m2) u2

v1 = (m + M + M/m)u1

therefore,

mu1 = (m + M)(m + M + M/m)u1

m2 = (m + M)((m2 + Mm + M)

m2 = m3 + Mm2 +Mm +Mm2 + M2m + M2

M2(m + 1) + M(2m2 + m) + m3 - m2 = 0

now take the roots, you will get your relation

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