Question

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

A. 4.0 cm, 59 degrees West of the South axis
B. 9.7 cm, 31 degrees West of the South axis
C. 8.2 cm, 60 degrees South of the West axis
D. 5.8 cm, 31 degrees South of the West axis

I know how to do it, but forgot my protractor at home... pls help

Answer 1

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

Step-by-step 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=√(v_1^2+v_2^2)=√(5.0^2+3.0^2)=5.8 cm`

The direction can be found as follows:

`\theta=tan^(-1)((v_2)/(v_1))=tan^(-1)((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.