Question

You travel 7 m E on a unicycle. You then turn and travel 30 m N. You trip up a bit and roll

back 6 m S. What is your displacement from the starting point written as a single.
vector?

Answer 1

(7, 24)

Magnitude = 25

Angle = 73.74°

Step-by-step explanation:

On a coordinate system, assuming the starting coordinate is (0, 0), 7 m East will locate the cyclist at coordinate (7, 0)

30 N will locate her at (7, 30)

6 m S = going down 6 on the y-coordinate

So the final position is (7, 24)

A vector drawn from (0,0) to (7, 24) can be represented as (5, 24)

The magnitude of this vector is

`|\vec v| = √(a_x^2 + a_y^2)\\\\|\vec v| = √((7)^2 + (24)^2)\\\\|\vec v| = √(49 + 576)\\\\|\vec v| = √(625)\\\\|\vec v| = 25`

`\text{Angle = } \tan^(-1)\left((24)/(4)\right) = 73.74^\circ`