Answer:
magnitude = 161.3m, ∅ = 32.9°
Explanation:
Vector addition always works the same. Add two vectors by adding their respective components.
vector A: [tex]\left[\begin{array}{c}85.0&0.0\end{array}\right][/tex]
vector B:[tex]101.0\left[\begin{array}{c} cos60.0&sin 60.0\end{array}\right] =\left[\begin{array}{c}50.5&87.5\end{array}\right][/tex]
Adding vector A and B: [tex]\left[\begin{array}{c}85.0&0.0\end{array}\right] +\left[\begin{array}{c}50.5&87.5\end{array}\right] = \left[\begin{array}{c}135.5&87.5\end{array}\right][/tex]
The magnitude of any vector [tex]\left[\begin{array}{c}a&b\end{array}\right][/tex] is given by the Pythagorean theorem:
[tex]magnitude = \sqrt{a^2+b^2}[/tex]
In the case of the vector A+B:
[tex]magnitude = \sqrt{135.5^2+87.5^2}[/tex]
The angle ∅ of the vector can by found by using trigonometric functions:
For instance, the angle ∅ for a vector [tex]\left[\begin{array}{c}a&b\end{array}\right][/tex] is given by the equation:
[tex]tan\phi= \frac{b}{a}[/tex]
The direction ∅ can be found by solving the trigonometric function.
In the example of vector A+B:
[tex]tan\phi = \frac{87.5}{135.5}[/tex]
Solving for ∅:
[tex]\phi = tan^{-1} (\frac{87.5}{135.5})=32.9[/tex]
