Can I prove elastic impulse like that? [closed]

This is not a homework question, I have got the correct solution; My question is about: "Why does my kind of solution not work?"

Given the following:

• mass 1: 5kg, velocity 1: 4m/s in positive x direction
• mass 2 : 10kg, velocity 2: 3m/s in negative x direction
• mass 2 stopped after collision

question: is the collision elastic?

answer from the book (to proof that I do not try to solve homework): "No because $\Delta E_{kin}=-75Joule$

My trial was different and I just wonder if I could have done it like this:

Since mass 2 stopped after collision, I used a formula for elastic collision:

$v_{2,final}=\frac{2m_{1}}{m_{1}+m_{2}}*v_{1,initial}$

$0=\frac{2*5kg}{5kg+10kg}*4m/s$ => you can clearly see that this equation doesn't work so, I argued that it is not elastic. Am I correct with this method?

• Yes it's quite correct. – Jnan Mar 26 '18 at 17:10
• How would you know $\Delta E$? – pfnuesel Mar 27 '18 at 0:01
• @pfnuesel - from conservation of momentum to get the final velocity of mass 1 then calculation of the total kinetic energy at the end for masses 1 and 2 compared to the initial kinetic energies of masses 1 and 2 – tom Mar 27 '18 at 22:15