Question

Find the resultant force when

F1 = 50 N and F2 = 20 N
(F1 is vertical and F2 is horizontal. It looks like it's a graph and there's a diagonal line going between them and the line is labeled "Resultant".

Answer 1

The resultant is the vector sum of the sum of each component. The components are perpendicular, like an x-y graph. Since you only have two components altogether, your resultant is the sum of 50N along y, and 20N along x. It's given simply by


`F_(res)=20 a_x + 50a_y`

where
`a_x` is the unit vector along x and
`a_y` is the unit vector along y. The magnitude of
`F_(res)` is given by the Pythagorean theorem as


`|F_(res)|= √(20^2+50^2)=53.85N`

Its angle above the x-axis is given by the arctangent of the y-component divided by the x-component:


`\theta = tan^(-1)( (50)/(20))=68.2 \deg`