# Question 1a6bb

Jul 19, 2017

Relation is great.

#### Explanation:

Suppose,a particle of mass ${m}_{1}$ moving with a velocity of ${u}_{1}$ collides with a particle of mass${m}_{2}$ moving with a velocity ${u}_{2}$.
After collision the speed of the mass ${m}_{1}$ and${m}_{2}$ are respectively ${v}_{1}$ and ${v}_{2}$.

Let,the ${m}_{1}$ particle pushes the other with the force${F}_{1 \to 2}$ and the ${m}_{2}$ particle on ${m}_{1}$ is F_(2->1#.
According to Newton's third law,
${F}_{1 \to 2} = - {F}_{2 \to 1}$
As we know impulse of force is equal to change of momentum ,so we can write
${F}_{1 \to 2} = {m}_{1} {u}_{1} - {m}_{1} {v}_{1}$
${F}_{2 \to 1} = {m}_{2} {u}_{2} - {m}_{2} {v}_{2}$
Solving all equations,
${m}_{1} {u}_{1} - {m}_{1} {v}_{1} = - {m}_{2} {u}_{2} + {m}_{2} {v}_{2}$
$\implies {m}_{1} {u}_{1} + {m}_{2} {u}_{2} = {m}_{1} {v}_{1} + {m}_{2} {v}_{2}$
That's the all.