Question

If a force of 40N acting in the direction due east and a force of 30N acting In the direction due north. The magnitude of the resultant force will be

Answer 1

`\begin{gathered} Given:force\text{ in east direction= 40N} \\ force\text{ in north direction=30N} \\ resultant\text{ force=?} \end{gathered}`
`\begin{gathered} the\text{ resultant of two forces is given by the following formula} \\ \vec{F}=\sqrt{F_1^{\vec{}2}+F_2^2+2F_1F_2cos}\theta \\ here\text{ F= resultant force acting on the body } \\ and\text{ F}_1\text{ and F}_{2\text{ }}are\text{ individual forces acting on the body.} \\ \theta=\text{ angle between the individual forces} \end{gathered}`
`\begin{gathered} here,\text{ let F}_1=40N \\ F_2=30N \\ since\text{ the angle between the east and north is 90}\degree\text{ so the angle between} \\ F_1\text{ and F}_{2\text{ }}\text{ is 90}\degree \\ so\text{ cos90}\degree=0 \\ by\text{ putting all the values in the above formula we get} \\ \vec{F}=√(40^2+30^2+0)\text{ N} \\ \vec{F}=\sqrt[]{2500}\text{ N} \\ F=50N \end{gathered}`

So the magnitude of the resultant force is 50N