Question

A group of hikers walks 2 miles east and then 1 mile north. After taking a break, they then hike 4 miles east to their final destination. What vector describes their hike from their starting position to their final destination? Let 1 unit represent 1 mile.

Answer 1

The vector that describes their hike from their starting position to their final destination is < 6, 1 >

Answer 2

Intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

Explanation:

Required vector is consists of the two components

vx= 2+4=6 units and vy= 1 unit and vx ⊥ vy

We will use Pythagorian theorem to find intensity of the vector v

v∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 units

The angle ∡α between vector and east direction we wil find with tanα

tanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

Good luck!!!