The magnitude and the direction angle for the resultant vector are 10N and 120degrees respectively
The formula for calculating the resultant vector is expressed as:
[tex]R^2 = u^2 + v^2\\R =\sqrt{u^2+v^2}[/tex]
Given the following distances:
u = -5√3 feet (west direction)
v = 5 feet
Substitute the given values into the formula above;
[tex]R=\sqrt{(5\sqrt{3} )^2+5^2} \\R=\sqrt{(25 \times 3)+25}\\R=\sqrt{75 + 25}\\R=\sqrt{100}\\R = 10 feet[/tex]
The magnitude of the resultant vector is 10feet
Get the direction:
[tex]\theta = tan^{-1}\frac{y}{x} \\\theta = tan^{-1}\frac{5}{-5\sqrt{3} }\\\theta =tan^{-1}\frac{-1}{\sqrt{3} }\\\theta = -60^0[/tex]
Since tan is negative in the second quadrant, hence;
[tex]\theta = 180 - 60\\\theta = 120^0[/tex]
Hence the magnitude and the direction angle for the resultant vector are 10N and 120degrees respectively.
Learn more here: https://brainly.com/question/5177683
