Question

What is the resultant displacement of the two vectors below? Vector 1: 5.0 cm, W Vector 2: 3.0 cm, S

Answer 1

Answer:

D. 5.8 cm, 31 degrees South of the West axis

Explanation:

Here we have two vectors:

$v_1 = 5.0 cm$ direction west

$v_2 = 3.0 cm$ direction south

We note that the two vectors are perpendicular, so we can use the Pythagorean's theorem to find the magnitude of their resultant:

$v=\sqrt{v_1^2+v_2^2}=\sqrt{5.0^2+3.0^2}=5.8 cm$

The direction can be found as follows:

$\theta=tan^{-1}(\frac{v_2}{v_1})=tan^{-1}(\frac{3.0}{5.0})=31^{\circ}$

And according to how we calculated the ratio inside the formula, this angle is measured as south of west.