Question

A 65.75 lb child is sitting on a teeter board at(-1,-4) and the fulcrum is at (6.5, 3.5) where units are in feet. At what point should a 39.4 lb child sit to be in equilibrium?

Answer 1

Use the formulae (x-x1)/(x2-x1)=M2/(M1+M2), (y-y1)/(y2-y1)=M2/(M1+M2) (see the question about the two children weighing 22 and 47.5 kilos, showing a representative diagram and derivation of the formulae). We have x=6.5, y=3.5, M1=65.75lb, M2=39.4lb, x1=-1, y1=-4. M1+M2=105.15lb.

(6.5+1)/(x2+1)=39.4/105.15=(3.5+4)/(y2+4).

Cross-multiplying:

105.15*7.5=39.4x2+39.4 and 105.15*7.5=39.4y2+39.4*4.

x2=19.016' and y2=16.016' approximately. So the coordinates are (19.016,16.016) feet.