Need to work out how to calculate the time to collision for two objects! I have

Question

Need to work out how to calculate the time to collision for two objects!

I have 2 balls of mass m1=1 kg, m2=2kg. The first starts at x=0 and has initial velocity v1i=2 m/s. The second ball starts at x=5 and has an intial of velocity of v2i=0.5 m/s. I needed to calculate the final velocities which were v1f=0, and v2f=1.5 m/s, which are the correct answer. I need to calculate out the time up until collision which is supposed to be around 3 seconds, but I can't figure out the work for it. This is an elastic collision. Please help!

Explanation / Answer

final velocities after the colision

V1f =[ (m1-m2)V1i + (2m2)V2i ] / (m1+m2)

V1f = [ (1-2)2 + 2*2*0.5 ]/(1+2) = [ -2 + 2 ]/(3) = 0 m/s

second particle velocity is

V2f = [ (m2-m1)V2i + 2m1*V1i ] /(m1+m2)

V2f = [(2-1)0.5 + 2*1*2] /(1+2) = 4.5/3 = 1.5 m/s

time taken for the collision to occur = 5/1.5 = 3.3 s

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