Question

One force vector points in the -x direction and has magnitude 900 newtons (N). We don't know the

second force vector, but we know that the sum of the two is a vector pointing exactly in the

+y direction, with magnitude 100 N. Describe the unknown second force vector by a) giving

its components along the x and y axes (including the correct sign), and b) giving its

magnitude and its direction, where zero degrees is in the +x direction and positive angles go

counterclockwise.

Answer 1

(a) The sum of the two forces is given and one of the force vector is given.

from the figure : the x component of the force is exactly equal to the given force because the resulting force is in the y direction.

Let us assume the F(2) is the unknown force.

Let us assume the force is angle $\theta$ from the +ve X direction,

so; F(2) * Cos($\theta$) = 900

F(2) * Sin($\theta$) = 100

divide both the equations : tan($\theta$) = 1/9

thus   $\theta$ = 6.3 Degrees

squaring and adding both the equations :

F(2)*F(2) = 810000 + 10000 = 820000

F(2). = 905.53 N.

X component of force is 900 N in +X direction.

Y component of force is 100 N in +y direction.

Force magnitude is 905.53 N with the angle 6.3 degrees from the +X direction.