30.8 m
Step-by-step explanation:
Given: [tex]V = 43\:\text{m}[/tex], [tex]V_y = 30\:\text{m}[/tex]
The x-component of vector [tex]\vec{\text{V}}[/tex] is
[tex]V_x = \sqrt{V^2 - V_y^2} = \sqrt{(43)^2 - (30)^2} = 30.8\:\text{m}[/tex]
The x- component of the vector is 30.8meters.
If [tex]v = < a. b >[/tex] be a position vector then the magnitude of vector v is found by [tex]|v| =\sqrt{a^{2}+b^{2} } }[/tex] , where a and b are the x and y component respectively.
And the direction is equals to the angle formed x- axis or y axis.
According to the given question
We have
Magnitude of the vector, |v| = 43meters
Y- component of the vector, b = 30meters
Since, we know that
[tex]|v| =\sqrt{a^{2} +b^{2} }[/tex]
Substitute the value of |v| = 43 and b = 30 in the above formula of magnitude.
⇒ [tex]43 = \sqrt{a^{2}+30^{2} }[/tex]
⇒ [tex]43 = \sqrt{a^{2}+900 }[/tex]
⇒ [tex]43^{2} =a^{2} + 900[/tex]
⇒ [tex]1849 = a^{2} + 900[/tex]
⇒ [tex]1849-900=a^{2}[/tex]
⇒ [tex]949=a^{2}[/tex]
⇒ [tex]a =\sqrt{949}[/tex]
⇒ [tex]a = 30.8[/tex]
Hence, the x- component of the vector is 30.8meters.
Learn more about magnitude and direction of a vector here:
https://brainly.com/question/13134973
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