The direction of the net displacement is [tex]53.5^{\circ}[/tex]
Explanation:
In order to find the net displacement, we have to resolve each of the two displacements into the x- and y- directions.
The first displacement is:
[tex]d_1 = 11.1 m[/tex] at [tex]62.4^{\circ}[/tex]
Resolving into both directions,
[tex]d_{1x}=(11.1)(cos 62.4^{\circ})=5.1 m\\d_{1y}=(11.1)(sin 62.4^{\circ})=9.8 m[/tex]
The second displacement is
[tex]d_2=53.4 m[/tex] at [tex]51.7^{\circ}[/tex]
Resolving into both directions,
[tex]d_{2x}=(53.4)(cos 51.7^{\circ})=33.1 m\\d_{2y}=(53.4)(sin 51.7^{\circ})=41.9 m[/tex]
So, the x- and y-components of the net displacement are
[tex]d_x=d_{1x}+d_{2x}=5.1+33.1=38.2 m\\d_y=d_{1y}+d_{2y}=9.8+41.9=51.7 m[/tex]
And so, the direction with respect to the positive x-axis, expressed as a counter-clockwise angle, is:
[tex]\theta=tan^{-1}(\frac{d_y}{d_x})=tan^{-1}(\frac{51.7}{38.2})=53.5^{\circ}[/tex]
Learn more about displacement:
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