1. Vector Addition

2. Vector Addition Vectors can be added together to find the result
Resultant: a vector representing the sum of two or more vectors

3. Vector Addition: One-dimension
What is the turtle’s displacement?
KEY POINT: When finding the resultant in ONE-DIMENSION, add when going in the same direction and subtract when going in opposite directions

4. Quick Checks

5. Practice Problem
An Angry bird slowly flies east with a velocity of 10 m/s relative to the ground. There is a 2 m/s wind pushing him forward. What is the birdie’s real velocity?

6. Vector Addition: Two-Dimensions
Dotted line = Resultant
*Always connect tail of first vector to the head of the last

7. Draw the Resultants of the following vectors:
*Always connect tail of first vector to the head of the last

8. Vector Addition: Two-Dimensions
Just as you discovered in the treasure hunt activity, moving vectors around will produce the same resultant, as long as you don’t change their magnitude or direction

9. Vector Addition: Two Dimensions
An angry bird is flying north with a velocity of 4m/s. There is crosswind blowing east at 3m/s. Will the birdie speed up, slow down, or remain at the same velocity?
3 m/s east
4 m/s north
KEY POINT: When finding the resultant in TWO-DIMENSIONS, use Pythagorean theorem

10. a2 + b2 = c2 Pythagorean Theorem! 42 + 32 = c2 16 + 9 = c2 √25 = √c2
3 m/s east
4 m/s north
5 m/s northeast
The birdie will speed up.

11. Quick Checks
When adding vectors in 2-dimensions, always draw the resultant from ________ to ________
What did the treasure hunt yesterday teach us about the order of vectors in 2-dimensions?
How do we solve for the resultant vector in 2-dimensions?

12. Practice Problem
While following the directions on a treasure map, a pirate walks 45.0 m north, then turns and walks 7.5 m east. What single straight-line displacement could the pirate have taken to reach the treasure?

13. Work it Out!
A plane heads west with a velocity of 100km/h relative to the ground. There is a 20km/h headwind. What is the plane’s real velocity?
How fast will a boat that normally travels 10 km/h in still water be moving with respect to land if it sails directly across a stream that flows at 10 km/h?
A boat is traveling west with a velocity of 10 m/s. The river is flowing northward (it is the Nile) with a velocity of 3 m/s. What is the boat’s true velocity?

14. You Got This!
A seagull at South Padre Island flies east into a 15km/h headwind with a velocity of 15km/h. What is the gull’s velocity relative to the ground?
A truck driver attempting to deliver some furniture travels 8 km east, turns around and travels 3 km west, and then travels 12 km east to his destination.
What distance has the driver traveled?
What is the driver’s total displacement?
The current in a river is flowing south at a rate of 8 km/h. A fish is trying to swim west with a velocity of 4 km/h. What is the fish’s resultant speed and direction?