Question

A hiker walks 4 km north and then 5 km northeast. Draw displacement vectors representing the hiker's trip and draw a vector that represent

Answer 1

R = 8.33 km

, θ = 64.9⁰

Step-by-step explanation:

For this exercise, we can see the attachment.

The resulting displacement can also be found analytically, for this we find the displacement on each axis

Let's start with decompile [put the second displacement (L)

sin 45 = y2 / L

cos45 = x2 / L

y2 = L sin 45

x2 = L cos45

y2 = 5 sin 45 = 3.54 km

x2 = 5 cos 45 = 3.54 km

The components of the displacements are

X = x2

X = 3.54 km

Y = y1 + y2

Y = 4 + 3.54

Y = 7.54 km

In module this displacement is

R = √ X² + Y²

R = √ 3.54² + 7.54²

R = 8.33 km

We look for the angle with trigonometry

tan θ = Y / X

θ = tan⁻¹ Y / X

θ = tan⁻¹ 7.54 / 3.54

θ = 64.9