Vector Addition Vectors can be added together to find the result Resultant a vector representing the sum of two or more vectors Vector Addition Onedimension What is the turtles displacement ID: 615465
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Slide1
Vector AdditionSlide2
Vector Addition
Vectors can be added together to find the result
Resultant
: a vector representing the sum of two or more vectorsSlide3
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 directionsSlide4
Quick ChecksSlide5
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?Slide6
Vector Addition: Two-Dimensions
*Always connect tail of first vector to the head of the last
Dotted line =
ResultantSlide7
Draw the Resultants of the following vectors:
*Always connect tail of first vector to the head of the lastSlide8
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.htmlSlide9
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?
4 m/s north
3 m/s east
KEY POINT
: When finding the resultant in TWO-DIMENSIONS,
use
Pythagorean theoremSlide10
Pythagorean Theorem!
a
2
+ b
2
= c
2
42 + 32
= c
2
16 + 9 = c
2
√25 = √c
2 5 = c
4 m/s north
3 m/s east
5 m/s northeast
The birdie will speed up.Slide11
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?Slide12
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?Slide13
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?Slide14
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?