Vector Addition

Question

Draw and analytically solve:

The displacement vector F1 is directed to the East and has a magnitude of 3 m. The displacement vector F2 is directed to the North and has a magnitude of 4 m.

Using the scale 1.0 m = 1.0 cm, add the displacement vectors.

Answer 1

Edmond,

1. Start by sketching out the vectors
2. Draw F₁ to the east - I'm sure you can figure out how long it is
3. From the end of F₁, draw, F₂ towards the north. This is often called head-to tail addition.
4. The resultant displacement vector can be draw from the start/ "tail"of F₁ to the end/"head" of F₂
5. The magnitude/length of the resultant:
6. Use the Pythagorean Theorem
7. a² + b² = c²
8. 3² +4² = R²
9. The bearing is usually written as an angle from the x axis (East), so, using your diagram, here it's just the angle between F₁ and the resultant R
10. Use trig to find that angle - you can use any relationship since you know all 3 sides
11. tanθ = opp/adj
12. tanθ = 4 / 3

I'll leave the calculations to you.