Question

Two forces 20 N and 5 N are acting at an angle of 120° ° between them. Find the resultant force in magnitude and direction.​

Answer 1

Answer:

Two forces 20 N and 5 N are acting at an angle of 120° between them, the magnitude of the resultant force is $22.9N$ and the direction is $13.4$⁰ from vector A

Explanation:

The resultant of any two vectors A and B inclined to an angle $\alpha$ is given by the formula,

$R=\sqrt{A^{2} +B^{2} +2ABcos \alpha }}$

From the question, we have

the magnitude of vector A is $/A/=20N$

and that of vector B is $/B/=5N$

the angle between vector A and vector B is $\alpha =120$

substitute the given values in the equation we get

$R=\sqrt{25^{2} +5^{2} +2*25*5cos120} =22.91N$

The magnitude of the resultant is $R=22.91N$

the direction of the resultant is given by the formula

$tan\beta =\frac{Bsin\alpha }{A+Bcos\alpha }$

$=\frac{5sin120}{20+5cos120} =0.24$

$\beta =tan^{-1}(0.24)=13.4$