Question

A vector has the components Ax=29m and Ay=14m. (A) What is the magnitude of this vector? (B) What angle does this vector make with the positive x axis?

Answer 1

Answer:

$|A|=32.2048438m$

$\alpha =25.76932762 ^{\circ}$

Explanation:

In order to find the magnitude of the vector we need to use pythagorean theorem. As you can see in the picture I attached you, the components Ax and Ay represents the legs and the the hypotenuse is the magnitude of the vector A. Hence:

$|A|=\sqrt{(Ax^{2})+(Ay^{2}) } =\sqrt{(29)^{2}+(14)^{2} }=32.20248438m$

Now in order to find the angle $\alpha$  we only need to use  the trigonometry identity of tangent:

$tan(\alpha )=\frac{Ay}{Ax}$

Isolating $\alpha$

$\alpha =arctan(\frac{Ay}{Ax} )=arctan(\frac{14}{29} )=25.76932762 ^{\circ}$