Answer:
(a) 2.001N
(b) 2.001N
Explanation:
A sketch of the scenario has been attached to this response.
Since only the force vector Fâ is required, the only force shown in the sketch is Fâ.
As shown in the sketch;
The x-component of the force vector Fâ = [tex]F_{x}[/tex]
The y-component of the force vector Fâ = [tex]F_{y}[/tex]
The magnitude of Fâ as given in the question = 2.83N
The angle that the force makes with respect to the x-axis = 45.0°
Using the trigonometric ratio, we see that;
(a) cos 45.0° = [tex]\frac{F_x}{F_1}[/tex]
=>  [tex]F_{x}[/tex] =  Fâ cos 45.0°
=> [tex]F_{x}[/tex] =  2.83 cos 45.0°
=> [tex]F_{x}[/tex] = Â 2.83 x 0.7071
=> [tex]F_{x}[/tex] = Â 2.001N
(b) Also;
sin 45.0° = [tex]\frac{F_y}{F_1}[/tex]
=>  [tex]F_{y}[/tex] =  Fâ sin 45.0°
=>  [tex]F_{y}[/tex] =  2.83 sin 45.0°
=> Â [tex]F_{y}[/tex] = Â 2.83 x 0.7071
=> Â [tex]F_{y}[/tex] = Â 2.001N
Therefore, the x-component and y-component of the force vector Fâ is 2.001N
