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A particle of mass m collides elastically at an angle of 90 degrees with a lighter particle of mass km. Initially both particles had a speed u. After the collision the particles move apart both at an angle of 45 degrees from the initial path of the particle of mass m

show that k=sqrt(2)-1.

I tried using conservation of linear momentum in horizontal directions giving me 2 equations.

u=(v1^2 ^kv2^2)/sqrt(2)

ku=(v1 -kv2^2)/ sqrt(2)

where v1 is the final velocity of the particle of mass m and v2 is the final velocity of the particle of mass km.

I tried to upload a diagram I had drawn but it would not let me, sorry.

And conservation of kinetic energy tells us that (1+k)u^2=v1^2+v2^2 but I can't put it all together. Please help me