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Find the x- and y-components of the vector a⃗ = (19 m/s2 , 31 ∘ left of −y-axis).

Find the x- and y-components of the vector a⃗ = (19 m/s2 , 31 ∘ left of −y-axis).-example-1
User Alphonse
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1 Answer

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The value of the acceleration given is,


a=19ms^(-2)

The angle of the acceleration with the negative of the y-axis in the third quadrant is,


\theta=31^(\circ)

Solution:

The diagrammatic representation of the given system is,

The angle of the acceleration with the positive of the x-axis is,


\begin{gathered} \theta_1=31^(\circ)+90^(\circ) \\ \theta_1=121^(\circ) \end{gathered}

Thus, the component of the acceleration along the positive of the x-axis is,


\begin{gathered} a_x=a\cos (\theta_1) \\ a_x=19\cos (121^(\circ)) \\ a_x=-9.8ms^(-2) \end{gathered}

The angle of the acceleration with the positive of y-axis is,


\begin{gathered} \theta_2=(90^(\circ)-31^(\circ))+90^(\circ) \\ \theta_2=149^{^(\circ)} \end{gathered}

The y-component of the acceleration is,


\begin{gathered} a_y=a\cos (\theta_2) \\ a_y=19*\cos (149^(\circ)) \\ a_y=-16.29ms^(-2) \end{gathered}

Thus, the x and y-component of the acceleration are -9.8,-16.29.

Find the x- and y-components of the vector a⃗ = (19 m/s2 , 31 ∘ left of −y-axis).-example-1
User Aviran
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