Question

A vector of 10N makes an angle of $30^\circ $ with positive x-axis. Find its components along the x-axis and y-axis.

Answer 1

Hint: Vector resolution is a method in which a single vector is broken down into two or more smaller vectors. We need to apply vector resolution to find the component along the x axis and the y axis. Here the vector is at a 30 degree angle.


Complete step by step solution:

Here the vector can be broken down into two components one would be in x axis and another would be in y axis.
${F_x} = 10\cos \theta $;
The angle the axis is making with the vector would always be $\cos \theta $.
Now, we need to resolve for y axis:
${F_y} = 10\sin \theta $;
Now, we know the angle so, put it in the horizontal component as well as in vertical component.
${F_x} = 10\cos 30^\circ $;
$ \Rightarrow {F_x} = 10 \times \dfrac{{\sqrt 3 }}{2}$;
The horizontal component of the given vector is:
$ \Rightarrow {F_x} = 5\sqrt 3 $;
Now, the similar case is with the vertical component:
${F_y} = 10\sin 30$;
$ \Rightarrow {F_y} = 10 \times \dfrac{1}{2}$;
The vertical component is:
$ \Rightarrow {F_y} = 5$;

Therefore, the horizontal and vertical components have been resolved and they are given as: horizontal component is ${F_x} = 5\sqrt 3 $ and the vertical component is ${F_y} = 5$.

Note: Here I need to draw a graph and since there is no mentioning about the starting point of the vector in regard x axis or y axis so draw the vector at (0,0). Now, the axis that is not making an angle with the vector will always be sin and the vector which is making an angle with the vector would always be cosine.