Vector Voyages Slides
Vector Voyages
Mastering Navigation through Vector Addition and Bearings
Lesson Objective
Master Bearings
Convert between mathematical standard angles and navigational bearings.
Vector Addition
Calculate resultant velocities (ground speed) by summing plane and wind vectors.
Target: High School Math (11th Grade)
Warm-up: Compass Drill
5 MIN
North
Southeast
Bearing 200°
Sketch these vectors on your scratch paper using a standard x-y coordinate plane.
Navigation Application
Embedded media
Watch Segment: 4:15 - 10:41
Focus: Plane velocity & Wind resultant
Bearing vs. Math Angles
Standard Math
- Start at Positive X-Axis (East)
- Rotate Counter-Clockwise
Navigational Bearing
- Start at North (Positive Y-Axis)
- Rotate Clockwise
Board Practice: River Crossing
"A boat travels at 15 mph due North across a river. The river current is 4 mph flowing East. What is the boat's resultant velocity?"
Step 1: Component Form
Boat: \(\vec{v}_b = \langle 0, 15 \rangle\)
River: \(\vec{v}_r = \langle 4, 0 \rangle\)
Step 2: Add Vectors
\(\vec{v}_{res} = \langle 4, 15 \rangle\)
Ground Speed
\(|v| = \sqrt{4^2 + 15^2}\)
\(|v| \approx 15.52 \text{ mph}\)
Bearing
\(\tan(\theta) = \frac{x}{y} = \frac{4}{15}\)
\(\theta \approx 14.93^\circ\)
Exit Ticket
Apply what you've learned. Calculate the ground speed and bearing of a plane flying through crosswinds.
Materials
Scientific Calculator
Submission
Submit before leaving
Vector Voyages Exit Ticket
Exit Ticket
Topic: Vector Navigation & Ground Speed
Name:
Date:
Flight Scenario
A small aircraft is flying due North at an airspeed of 420 mph. A crosswind is blowing from the West at 45 mph.
1. Vector Visualization
[Sketch plane and wind vectors]
N
S
W
E
2. Vector Components
Write the component form \(\langle x, y \rangle\) or \(i, j\) form for both vectors.
Plane Vector (\(\vec{P}\))
Wind Vector (\(\vec{W}\))
3. Resultant Velocity (Ground Speed)
Calculate the magnitude of the resultant vector. Round to the hundredths place.
Final Ground Speed:
mph
4. Final Bearing
Calculate the navigational bearing relative to North (clockwise).
Navigational Bearing:
degrees
Ensure your calculator is in Degree mode.
Show all work for partial credit.
