Question

There are two forces each of magnitude 10 units. One inclined at an angle of ${30}^0$ and the other at an angle of ${135}^0$ to the positive direction of x-axis. The x and y components of the resultant are respectively.

Answer 1

Let first force be $F_1$ and its magnitude $=10$

Let first force be $F_2$ and its magnitude $=10$

Now,

Angle $F_1$ is making with positive x-axis $={30}^o$

Angle $F_2$ is making with positive x-axis $={135}^o$

Angle between $F_1$ and $F_2=135-30$

$={105}^o$

Since both the vectors have equal magnitude the resultant will make ${\frac{105}{2}}^o$.

Angle with both the vector $=52.5+30={82.5}^o$

Now, magnitude of resultant $=\sqrt{100+100+200\cos 105}$

$=12.175unit$

Now,

X component $=|R|\cos \theta$

$=12.175\times \cos 82.5$

$=12.175\times 0.13$

$=1.583$

Y component $=|R|\sin \theta$

$=12.175\times \sin 82.5$

$=12.175\times 0.99$

$=12.05$