$1.$ Balancing forces on a Seesaw: A parent of mass m$1=60$ kg sits on a uniform beam seesaw of mass M $=40$ kg$,$ at a distance r$1=1\mathrm{.}0$ m to the right of the pivot P $($as pictured below$).$ Each end of the beam is equidistant from P$.$  

a$)$ What distance r$2$ to the left of P should a child of mass m$2=30$ kg sit in order to balance the seesaw $($take the seesaw to be uniform$)?$ Show any equations you use or justify your intuition.

b$)$ What is the torque exerted by the weight of the parent, the torque from the childs weight, and the torque from the seesaw weight $($magnitude and direction for each case, with direction indicated as into or out of the paper$)?$