Question

the resultant of two equal forces acting at right angles is 2828N. Find the magnitude of each force

Answer 1

Let us suppose the two forces be F.
The angle between them is equal to 90^o.
The resultant force is given as:
$$\begin{gathered} R=\sqrt{F^2+F^2+2F^2\cos {90}^o}=\sqrt{2}F \\ \Rightarrow F=\frac{R}{\sqrt{2}}=\frac{2828}{\sqrt{2}}=1414\sqrt{2}\text{N} \end{gathered}$$
Therefore, the magnitude of each force is $1414\sqrt{2}\text{N}$