Question

The qreatest & the least resultant of two forces acting at a point are 29 N and 5N respectively. If each force is in aw eased by 3 N find the resultant of the two new forces acting at right angle to each other and obtain its direction also? (10m)

Answer 1

If initial force are $\overrightarrow{a}$ and $\overrightarrow{b}$

Then greatest resultant is $a+b$ and least is $a-b$

$⟹a+b=29$

and $a-b=5$

$⟹a=17N$ and $b=12N$

After increasing each by $3N$, $A=20N$ and $B=15N$

And resultant of new forces acting at right angle is

$F=\sqrt{A^2+B^2}=\sqrt{{20}^2+{15}^2}$

$⟹F=25N$

$\tan \theta =\frac{A}{B}=\frac{20}{15}=\frac{4}{3}$

$⟹\theta ={53}^o$ with vector $\overrightarrow{B}$