An `80 kg` boy and his `40 kg` sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with velocity `3.0 m//s` towards the west. Ignore friction, (a) Describe the subsequent motion of the girl. (b) How much chemical energy is converted into mechanical energy in the girl's muscles? (c) Is the momentum of the boy-girl system conserved in the pushing apart process? How can it he with no motion beforehand and plenty of motion afterward?

Explanation

Whomsoever we consider the aggressor, brother and sister exert equal in magnitude oppositely directed forces on each other, to give each other equal magnitudes of momentum. We take the eastward component of the equation Total original momentum `=` total final mom for the two-sibling system
`0=80kg(-3m//s)+(40kg)vimpliesv=6.0m//s`
i.e. she moves at `6.0 m//s` east.
b. Original chemical energy in the girl's body total final kinetic energy
`U_("chemical")=(1/2)(80kg)(3m//s)^(2)+(1/2)(40kg)`
`(6.0m//s)^(2)=1080J`
c. System's momentum is conserved with the value zero. The net forces on the two siblings are of equal magnitude and opposite directions. Their impulses add to zero. Their final momenta are of equal magnitude in opposite directions, to add as vectors to zero.