1. Honors Precalculus 4/24/18 IDs on and showing.
Check-in Direction Angle and Components.
Questions on Direction Angles and Components.
Complete Combinations of Vectors and Resultant Vectors.

2. Section 6.1 Combination of Vectors Resultant Vectors
Honors PreCalculus
Section 6.1
Combination of Vectors
Resultant Vectors

3. Example 1: A boat is traveling due West at a speed
of 20 mph. There is an 8 mph current flowing at a
bearing of 60º. What is the “true” speed of the boat? N
Step 1:
Resolve each vector into its components
60º
8mph
20 mph

4. Example 1: A boat is traveling due West at a speed
of 20 mph. There is an 8 mph current flowing at a
bearing of 60º. What is the “true” speed of the boat? N
Step 2:
Add horizontal components;
Add vertical components.
In other words; add the vectors
8mph
20 mph
So, the boat’s “true” speed due West is mph.
Without compensating for the current (by steering into it),
it’s traveling 4 mph North.

5. Example 1: A boat is traveling due West at a speed
of 20 mph. There is an 8 mph current flowing at a
bearing of 60º. What is the “true” speed of the boat? N
The resultant vector shows the actual
direction of the boat, without
compensating for the current

6. Example 2: An airplane is flying 350 mph at a bearing of 132º.
If the wind is blowing 47 mph at a bearing of 300º, find:
the actual (“ground”) speed of the plane and
the bearing of the plane as a result of the wind N
150º 47
132º
318º
300º
350

7. Example 2: An airplane is flying 350 mph at a bearing of 132º.
If the wind is blowing 47 mph at a bearing of 300º, find:
the actual (“ground”) speed of the plane and
the bearing of the plane as a result of the wind N
150º 47
318º
350

8. Example 2: An airplane is flying 350 mph at a bearing of 132º.
If the wind is blowing 47 mph at a bearing of 300º, find:
the actual (“ground”) speed of the plane and
the bearing of the plane as a result of the wind N
a) “ground” speed of the plane is
the magnitude of the resultant vector
b) Direction angle of resultant vector
Bearing:

9. Example 3: Three forces all work on the same object.
Force 1 = 100 lb at an angle of 50º
Force 2 = 50 lb at an angle of 160º
Force 3 = 80 lb at an angle of -20º
Find the resultant force, and the angle at which it acts. N
100
160º
50º 50
-20º 80