Four horizontal forces act on a vertical quarter$-$circular plate of radius $250$ mm$.$ Determine the magnitude and point of application of the resultant of the four forces if P$=$

$70$ N$.$

A figure shows forces applied on a vertical quarter$-$circular plate in the y$-$z plane.The plate lies in the y$-$z plane with the center at the origin where force P is applied in the negative x direction. The other three forces are applied at the edge of the plate. At the top of the plate on the y$-$axis, a $120-$newton load is applied in the positive x direction. A $200-$newton load acting in the positive x direction is applied $250$ millimeters from the origin along the z$-$axis. An $80-$newton load is applied in the negative x direction $30$ degrees from the y$-$axis.

The magnitude of the resultant force is

$170$

N$.$

The point of application of the resultant force is at y$=$

$235\mathrm{.}29$

mm$,$ z$=$

$74\mathrm{.}584$

mm$.$