Answer
Verified
377.7k+ views
Hint: A vector can be divided into two components along two perpendicular axes, those are called the rectangular components. Since the displacement is a vector quantity it also has the resolution along two axes. The values of the two components are cosine and sine of the angle multiplied with the magnitude of the vector. Note that, here the angle is the angle between the vector and the horizontal component.
Complete step by step answer:
In a two-dimensional coordinate system, any vector is broken into x -component and y -component. for instance, the vector \[V\] is broken into \[2\] elements, \[{V_x}\] and \[{V_y}\] . If the angle between the vector and its x -component be \[\theta \]
\[{V_x} = V\cos \theta \]
\[{V_y} = V\sin \theta \]
Here, displacement is a vector quantity. Let, the displacement vector is . given that, the angle between the vector and its x -component be \[\theta = 30^\circ \]
vector \[S\] is broken into two elements, \[{S_x}\] and \[{S_y}\].
\[{S_x} = S\cos \theta \]and \[{S_y} = S\sin \theta \]
Given, the magnitude of , \[S = 100\]
So, \[{S_x} = S\cos \theta = 100\cos 30^\circ \]
\[ \Rightarrow {S_x} = 100 \times \dfrac{{\sqrt 3 }}{2}\]
\[ \Rightarrow {S_x} = 50\sqrt 3 \]
And, \[{S_y} = S\sin \theta = {\text{100}}\sin 30^\circ \]
\[ \Rightarrow {S_y} = 100 \times \dfrac{1}{2}\]
\[ \Rightarrow {S_y} = 50\]
Hence, the horizontal and vertical components of the \[100m\] displacement will be \[ \Rightarrow {S_x} = 50\sqrt 3 \] and \[ \Rightarrow {S_y} = 50\]respectively.
Note: If we want to break the vector \[V\] along this vector itself i.e along the vector \[V\], the angle between the vector and its x -component will be \[\theta = 0^\circ \],
Such as, \[{V_x} = V\cos 0^\circ = 0\]
And, the vertical component will be \[{V_y} = V\sin 0^\circ = 0\]
From these we can conclude:
The value of the component of a vector along this particular vector will be the same as the magnitude of the vector.
There will be no vertical component of the vector in this case.
Complete step by step answer:
In a two-dimensional coordinate system, any vector is broken into x -component and y -component. for instance, the vector \[V\] is broken into \[2\] elements, \[{V_x}\] and \[{V_y}\] . If the angle between the vector and its x -component be \[\theta \]
\[{V_x} = V\cos \theta \]
\[{V_y} = V\sin \theta \]
Here, displacement is a vector quantity. Let, the displacement vector is . given that, the angle between the vector and its x -component be \[\theta = 30^\circ \]
vector \[S\] is broken into two elements, \[{S_x}\] and \[{S_y}\].
\[{S_x} = S\cos \theta \]and \[{S_y} = S\sin \theta \]
Given, the magnitude of , \[S = 100\]
So, \[{S_x} = S\cos \theta = 100\cos 30^\circ \]
\[ \Rightarrow {S_x} = 100 \times \dfrac{{\sqrt 3 }}{2}\]
\[ \Rightarrow {S_x} = 50\sqrt 3 \]
And, \[{S_y} = S\sin \theta = {\text{100}}\sin 30^\circ \]
\[ \Rightarrow {S_y} = 100 \times \dfrac{1}{2}\]
\[ \Rightarrow {S_y} = 50\]
Hence, the horizontal and vertical components of the \[100m\] displacement will be \[ \Rightarrow {S_x} = 50\sqrt 3 \] and \[ \Rightarrow {S_y} = 50\]respectively.
Note: If we want to break the vector \[V\] along this vector itself i.e along the vector \[V\], the angle between the vector and its x -component will be \[\theta = 0^\circ \],
Such as, \[{V_x} = V\cos 0^\circ = 0\]
And, the vertical component will be \[{V_y} = V\sin 0^\circ = 0\]
From these we can conclude:
The value of the component of a vector along this particular vector will be the same as the magnitude of the vector.
There will be no vertical component of the vector in this case.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE