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How to add vectors and calculate the resultant vector's magnitude and direction. It also introduces the concept of vector components, specifically in the context of projectile motion. Students will learn how to identify and calculate horizontal and vertical components of velocity.
Typology: Exams
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Ch. 5 in your text book
Students will be able to:1) Add smaller vectors going in the same direction to get one large vector for
that direction
horizontal and vertical vectors
Vectors have a
magnitude
and a
direction
. They are represented
by an arrow.
Longer vectors mean larger magnitudes, smaller vectors meansmaller magnitudes. The vectors don’t have to be next to each otherin order to add them, they just have to be going in the same direction.1m
1m 1m
1m
3m
1m
2m
Check for understanding: Add the vectors below
1m
1m 2m
1m
There is more than one correct way to add vectors. In the end, it is allthe same. Regardless of the path, you end up in the same place.
How would you add these two vectors?
You can add them, and it’s just likehow you drew a direct path fromschool to your final location on themap. This type of vector is called a resultant vector
Remember these vectors? What would the resultant vector look like?
We will not be doing lots of vectors like this, but you will see them inlater classes if you continue with math and science.
When something is thrown or shot, it has a velocity. That velocity isa vector and it is most likely at an angle to the ground. The vector isa resultant vector. The horizontal and vertical vectors that add to thatresultant are called components. There is a horizontal velocitycomponent and a vertical velocity component.
vH
v
v
v
θ
What does “component” mean?Component = a part/portion of something largerExample – A screen is one component of a phoneWith your partner, come up with a list of three components for differentthings. I’ll call on some of you to give your examples in a minute
For projectile motion, horizontal and vertical motion must be treatedindependently of each other; neither affect what happens to the other.Example:
https://www.youtube.com/watch?v=JCampZIwL5w
The velocity vector shows the direction of the object’s velocity. Aswe’ve discussed, if it’s moving at a constant velocity, the vectorwon’t change, but if the velocity is changing, the arrow will too.
Look at just the horizontal arrows. What do you notice?
No Δv = no acceleration. What is our equation for a constantvelocity?
H
This equation will be used for questions involving horizontal motion.
Look at just the vertical arrows. What do you notice?
Δv = acceleration. What is causing the acceleration?
v
2
This equation will be used for questions involving vertical motion.
The horizontal and vertical motions do not influence each other.Example: Say there are two, identical steel balls, that start at thesame height and begin to fall at the same time. If one is dropped andthe rolled off a ramp, which will hit the ground first?
Let’s go try it
All objects fall at the same rate. Wealso know that horizontal andvertical motions
do not
influence
each other. If you look at just thevertical motion, there is nodifference between the two spheres,so they land at the same time.
