Cogito
Precalculus · Chapter 3 · Lesson 3
Vector Applications
Forces, headings, and the resultant.
12 problems · about 22 minutes · TEKS P.4.G, TEKS P.4.J
What this lesson teaches
The student resolves vectors into components and finds resultants in force and navigation problems.
- Add vectors by components; magnitudes do not add.
- A vector of magnitude v at angle θ has components (v cos θ, v sin θ).
- Equilibrium means every component total is zero.
Warm Up
Straightforward practice. Get the method working first.
5 problemsForces (0, 5) and (12, 0) act together. Magnitude of the resultant?
Answer 13
Why 13.
Why can magnitudes not simply be added?
Answer Direction matters, so components must be added instead.
Why Vectors carry direction, so only components add.
(5, 2) + (1, 6). What is the y component?
Answer 8
Why 2 + 6.
Magnitude of (6, 8)?
Answer 10
Why √(36 + 64).
A vector of magnitude 10 at 0°. What is its x component?
Answer 10
Why 10 cos 0°.
Build It Up
The same ideas with more to keep track of.
3 problemsA vector of magnitude 10 at 90°. What is its x component?
Answer 0
Why 10 cos 90°.
A boat rows east at 12 and a current pushes north at 5. Resultant speed?
Answer 13
Why √(144 + 25).
Forces (4, 3) and (−4, −3). Magnitude of the resultant?
Answer 0
Why They cancel exactly.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsWhich quantities are vectors?
Answer Velocity; Force
Why A vector needs a direction as well as a size.
A plane flies north at 300 with a 40 westward wind. Resultant speed, to the nearest whole number?
Answer 303
Why √(90000 + 1600).
The Resultant: Forces (3, 0) N and (0, 4) N act together. What is the magnitude of the resultant, in newtons?
Answer 5 N
Why 5 N.
The Balance: Two forces are (6, −2) N and (−6, 2) N. What is the magnitude of the resultant, in newtons?
Answer 0 N
Why 0 N. The object is in equilibrium.