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Cogito

Precalculus · Chapter 3 · Lesson 3

Practice Worksheet

Vector Applications

Forces, headings, and the resultant.

12 problems · about 22 minutes · TEKS P.4.G, TEKS P.4.J

NameDate

Figure — use these to answer the problems

The dashed arrow shows the second vector starting where the first ends. Its tip is the resultant.
  • Vector a(3, 0)
  • Vector b(0, 4)
  • a + b(3, 4)
a, x component3
a, y component0
b, x component0
b, y component4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Forces (0, 5) and (12, 0) act together. Magnitude of the resultant?

    Answer

  2. Why can magnitudes not simply be added?

    • Direction matters, so components must be added instead.
    • Because of rounding errors.

  3. (5, 2) + (1, 6). What is the y component?

    Answer

  4. Magnitude of (6, 8)?

    Answer

  5. A vector of magnitude 10 at 0°. What is its x component?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. A vector of magnitude 10 at 90°. What is its x component?

    Answer

  2. A boat rows east at 12 and a current pushes north at 5. Resultant speed?

    Answer

  3. Forces (4, 3) and (−4, −3). Magnitude of the resultant?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Which quantities are vectors?

    • Velocity
    • Force
    • Mass
    • Temperature
    • Tick every box that applies.

  2. A plane flies north at 300 with a 40 westward wind. Resultant speed, to the nearest whole number?

    Answer

  3. The Resultant

    Forces (3, 0) N and (0, 4) N act together. What is the magnitude of the resultant, in newtons?

    AnswerN

  4. The Balance

    Two forces are (6, −2) N and (−6, 2) N. What is the magnitude of the resultant, in newtons?

    AnswerN