Answer:
The resultant force on the object = 16.65 N
Explanation:
The first force is 10N acting in in the direction N 45 degrees E
F₁ = 10N in the direction N 45 degrees E
The second force is 8N acting due South
F₂ = 8N due South
The diagram below illustrates the description
Resolve F₁ in the x and y direction
[tex]\begin{gathered} F_{1x}=10\sin 45 \\ F_{1x}=\frac{10}{\sqrt[]{2}} \\ F_{1y}=10\cos 45 \\ F_{1y}=\frac{10}{\sqrt[]{2}} \\ F_1=F_{1x}i+F_{1y}j \\ F_1=\frac{10}{\sqrt[]{2}}i+\frac{10}{\sqrt[]{2}}j \end{gathered}[/tex][tex]\begin{gathered} F_{2x}=0 \\ F_{2y}=8j \end{gathered}[/tex][tex]\begin{gathered} R_x=\sum ^{}_{}F_x \\ R_x=F_1x+F_2x \\ R_x=\frac{10}{\sqrt[]{2}}+0 \\ R_x=\frac{10}{\sqrt[]{2}} \end{gathered}[/tex][tex]\begin{gathered} R_y=\sum ^{}_{}F_y \\ R_y=F_{1y}+F_{2y} \\ R_y=\frac{10}{\sqrt[]{2}}+8 \end{gathered}[/tex][tex]\begin{gathered} R=R_xi+R_yj \\ R=\frac{10}{\sqrt[]{2}}i+(\frac{10}{\sqrt[]{2}}+8)j \\ |R|=\sqrt[]{(\frac{10}{\sqrt[]{2}})^2+(\frac{10}{\sqrt[]{2}}+8)^2} \\ R=\sqrt[]{50+227.14} \\ R=\sqrt[]{277.14} \\ R=16.65N \end{gathered}[/tex]
The resultant force on the object = 16.65 N 1
