Portfolio vectors and vector addition lab will make ! if 100%!
vectors and vector addition
today you are going to study vectors and use the gizmo simulation to visually graph vectors and to solve problems with them.
you will be using the adding vectors gizmo, provided by explore learning ()
procedure
open up the gizmo and run the simulation
to begin the simulation, play around with the simulation until you get an idea of what you are doing
some things to notice: to change the position of the arrow, click and drag the tail of the vector. to change the length and direction of the vector arrow, click and drag the head of the vector. to show the resultant vector of the two vectors added together, click the show resultant button.
the lab content
vectors are measurements that contain a magnitude and a direction. if you want to represent a vector graphically, you use an arrow. the direction of the arrow is the direction of the vector, the length of the arrow is the magnitude.
make vector a on the simulation have a magnitude of exactly 10 units.
what were the starting points and ending points of your vector?
pick two other starting and ending points for to make a vector that still has a magnitude of 10 units. write those points here
since vectors are defined by their direction and magnitude, what does having multiple starting and ending points to create the same vector tell you about how you can manipulate vectors on graphs?
part 2
adding vectors
to add vectors, you place them together with the head of one touching the tail of the other. you then draw a new vector, called the resultant vector, starting from the tail of the first and ending at the end of the second vector.
let’s test this
change vectors a and b to any size and direction you want.
press the “show resultant” button to have the resultant vector
prove that the resultant vector can be found by the method of adding vectors described above. how did you prove this?
part 3
vector components
every slanted vector can be said to be the sum of two other vectors that are straight. these straight vectors are often invisible and not drawn, so they must be draw in by hand. we call these vectors the ‘vector components’. the vector components must always be straight and one must be vertical, the other must be horizontal
set up vector a to be a straight vertical vector with a magnitude of 5 and vector b to be a straight horizontal vector with a magnitude of 6.
put them together head to tail and add them.
click on the resultant vector button to show the resultant vector.
can you place the resultant vector so that it stretches from the tail of one to the head of the other?
what shape do these three vectors make?
calculate the magnitude of the resultant vector
part 4:
now that you can see the relationship between the components and the resultant vectors, try answering the following questions. you will have to use the knowledge of trigonometric ratios you learned back in geometry to answer the following questions
question 1: vector 1 has a magnitude of 24 m and is pointed to the west. vector 2 has a magnitude of 11 and is pointed to the north. what is the magnitude and direction of the resultant vector produced by these two?
question 2
jeremy wants to buy some snacks. he walks four blocks east and two blocks south to get to the closest convience store to his house. how far away is store from his house, directly?
question 3
a slanted vector has a magnitude of 41 n and is at an angle of 23 degrees north of east. what are the magnitude and direction of the horizontal and vertical components of this vector?
question 4
a horizontal component vector has a magnitude of 11 m. if the resultant vector forms and angle with this component of 19 degrees, what is the magnitude of the resultant vector?