Question

A displacement vector has a magnitude of 810 m and points at an angle of 18° above the positive

x-axis. What are the horizontal and vertical components of this vector?

Answer 1

Answer:

horizontal component

$= 810 \cos(18)$

vertical component

$= 810 \sin(18)$

Answer 2

Answer:

The horizontal and vertical components of the displacement vector are 769.5m and 250.3m

Explanation:

Given that the magnitude of the displacement vector=810m

The angle made by the displacement vector with horizontal=18°

According to resolution of vectors,for a Vector of Magnitude R making an angle \alpha with horizontal,

The vertical and horizontal components are given as

$R _{x} = R \cos( \alpha ) \\ R _{y} = R \sin( \alpha )$

Therefore the horizontal component for given displacement vector is

$R _{x} = 810cos18 = 810 \times 0.95 = 769.5m$

The vertical component for given displacement vector is

$R _{y} = 810sin18 = 810 \times 0.309 = 250.3m$

Therefore,The horizontal and vertical components of the displacement vector are 769.5m and 250.3m

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