Question

Please derive it fastly
1. Conservation of momentum

Answer 1

let two ball of masses m1 and m2 moving in the same direction along a straight line path at initial velocity u1 and u2 respectively. on collision both balls exert equal and opposite force on each other and furhther move with velocities v1 and v2 respectively after collision.

initial momentum of m1=p1=m1u1

initial momentum of m2=p2=m2u2

total initial momentum =p1+p2=m1u1 + m2u2

Now after collision,
final momentum of m1=p1=m1v1

final momentum of m2=p2=m2v2
total final momentum=p1+p2
=m1v1+ m2v2

thus we have prove that
total initial momentum = total final momentum
when the body colllide with each other , by third law of newton (motion)
force exerted by m1 on m2= f12
=(m2v2-m2u2)/t
similarly force exerted by m2 on m1=
f21=(m1v1-m1u1)/t
by third law of motion
(m2v2-m2u2)/t=(m1v1-m1u1)/t
m2v2-m2u2=m1u1-m1v1
m1u1 +m2u2=m1v1+m2v2
(initial=final)momentum
proved