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9.4 (part 2): Applications with Vectors

9.4 (part 2): Applications with Vectors. Objectives. Solve problems using vectors and right triangle trigonometry. Applications. Vectors can be used to represent any quantity, such as force, that has magnitude and direction.

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9.4 (part 2): Applications with Vectors

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  1. 9.4 (part 2): Applications with Vectors

  2. Objectives • Solve problems using vectors and right triangle trigonometry.

  3. Applications • Vectors can be used to represent any quantity, such as force, that has magnitude and direction. • Velocity, weight and gravity are some quantities that physicists represent with vectors.

  4. Prep for Vector Application Problems: • You need to be able to draw a vector and represent a force as a vector. • A force with magnitude F and angle A can be written as <FcosA, FsinA>.

  5. Represent each force as a vector: • 1. A force of 130 N is applied at θ=30˚ • 2. A force of 25 N is applied at =135˚. • 3. A force of 12N at 30˚ from the horizontal.

  6. Example 1 Make a sketch to show the forces acting on a ship traveling at 23 knots at an angle of 17° with the current.

  7. Example 2 Find the magnitude and direction of the resultant vector for the diagram. 170 N 55° 300 N

  8. Example 3 A 100-newton force and a 50-newton force act on the same object. The angle between the forces measures 90°. Find the magnitude of the resultant force and the angle between the resultant force and the 50-pound force.

  9. Solution

  10. Example 4 Denzel pulls a wagon along level ground with a force of 18 newtons on the handle. If the handle makes an angle of 40° with the horizontal, find the horizontal and vertical components of the force.

  11. Solution

  12. Example 5 A 33-newton force at 90° and a 44-newton force at 60° are exerted on an object. What is the magnitude and direction of a third force that produces equilibrium on the object.

  13. Solution

  14. Example 6 Two ferry landings are directly across a river from each other. A ferry that can travel at a speed of 12 mph in still water is attempting to cross directly from one landing to the other. The current of the river is 4 mph. a. Make a sketch of the situation. b. If a heading of 0° represents the line between the two landings, at what angle should the ferry's captain head?

  15. Solution

  16. Homework Vector Application Problems Worksheet

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