A $71$kg parent and a $19$kg child meet at the center of an ice rink. They place their hands together and push on each other. The acceleration of the child has a magnitude of $2\mathrm{.}6$ m$/$s$^2.$

a$)$ draw a free body diagram for each person

b$)$ what is the force exerted on the child by the parent?

c$)$ what is the magnitude and direction of the parent's acceleration?