Question

Vector u has a magnitude of 5sq rt 3 feet and is directed due west. Vector v has a magnitude

Answer 1

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:

$R^2 = u^2 + v^2\\R =\sqrt{u^2+v^2}$

Given the following distances:

u = -5√3 feet (west direction)

v = 5 feet

Substitute the given values into the formula above;

$R=\sqrt{(5\sqrt{3} )^2+5^2} \\R=\sqrt{(25 \times 3)+25}\\R=\sqrt{75 + 25}\\R=\sqrt{100}\\R = 10 feet$

The magnitude of the resultant vector is 10feet

Get the direction:

$\theta = tan^{-1}\frac{y}{x} \\\theta = tan^{-1}\frac{5}{-5\sqrt{3} }\\\theta =tan^{-1}\frac{-1}{\sqrt{3} }\\\theta = -60^0$

Since tan is negative in the second quadrant, hence;

$\theta = 180 - 60\\\theta = 120^0$

Hence the magnitude and the direction angle for  the resultant vector are 10N and 120degrees respectively.

Learn more here: brainly.com/question/5177683