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. Vector Application Problems Worksheet
Homework
Vector Application Problems Worksheet