Question

"A hiker starts at point P and walks 2.0 kilometers due east and then 1.4 kilometers due north. The vectors in the diagram below represent these two displacements.

Using a protractor, determine the angle between east and the hiker’s resultant displacement"

Answer 1

Here, you need to use your "Protractor" as it is given in the question, but we can calculate the value with the help of our mathematical calculation too:
[ Protractor can be use only in real life, not here ]

Draw an imaginary line from initial position to final position.
Now, In that triangle, tan x = P/B
tan x = 1.4 / 2
tan x = 0.70
x = tan⁻¹ (0.70)
x = 35 [ tan 35 = 0.70 ]

In short, Your Answer would be 35 degrees

Hope this helps!

Answer 2

Magnitude = 2.44

Direction = 34.99°

Step-by-step explanation:

Resultant magnitude

`R = \sqrt {1.4^2+2.0^2}\\ R = √(1.96+4.0) \\ R=√(5.96)= 2.44`

The angle between the resultant displacement and the east can be calculated as follows:

`\theta = tan^(-1)(1.4)/(2.0)= 34.99^o`

The angle can be measured using protractor as well. Place the base of the protractor along the 2.0 km vector. Measure the angle along which the resultant line coincides with the base of the protractor.