Question

the resultant of two forces at a right angle to each other is 100N one of the forces makes an angle of 30 degree with that resultant what is the magnitude of this force​

Answer 1

Answer:

The resultant of two forces at a right angle to each other is $100N$. If $F_{1}$ makes an angle of $30^{\circ }$ with that resultant, then the magnitude of is  $F_1=15N$

Explanation:

The resultant of two vectors $A$ and $B$ inclined to an angle θ to each other is given by $R^2=A^2+B^2+2AB\cos \theta$

The resultant of two forces $F_{1}$ and $F_{2}$ is given by $F^2=F_1^2+F_2^2+2F_1F_2\cos \theta$

The angle between the two forces is $\theta =90^{\circ }$ (from the question two forces are right angle to each other).

Now, the resultant of two forces is,

$F^2=F_1^2+F_2^2$, since $cos90=0$

From the question resultant of the two forces is $F=100N$

Let the force$F_{1}$ makes an angle $\theta =30^{\circ }$with the resultant as shown in the figure.

When we write the resultant in the component form,

$F_1=F\cos 30$

Or $F\cos 30$ is the component of  resultant $F$ in the direction of $F_{1}$

$F_{1} =100 Cos30$$=15N$