Vector Addition

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

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

Quick Checks

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?

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

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

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 http://phet.colorado.edu/sims/vector-addition/vector-addition_en.html

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

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.

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?

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?

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?

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?