unit 5

Question 1

scalar

Answer 1

• magnitude/size
• no direction
• temp, distance, speed, mass

Question 2

vector

Answer 2

• quantity w/ magnitude and direction
• velocity, force

Question 3

what are vectors represented with

Answer 3

• directed line segments
• they have lengths (magnitude) nd direction (arrowhead)

Question 4

can magnitude can be negative?

Answer 4

no, always non-negative if in absolute value brackets

Question 5

how to draw/describe vectors in respect to horizontal

Answer 5

• draw: dotted horizontal line, angle goes COUNTER-CLOCKWISE
• describe: ___units at (degree) to the horizontal

Question 6

how to draw/describe vectors in true bearing

Answer 6

• draw: compass, angle measured from NORTH in CLOCKWISE
• describe: ___units at a true bearing of (degree)

Question 7

how to draw/describe vectors in quadrant bearing

Answer 7

• draw: compass, angle is in relation to north or south line
• describe: ___units at a quadrant bearing of [N80W]

Question 8

3 types of vectors

Answer 8

• parallel: same or opposite direction, wtvr magnitude
• equivalent: same magniude/direction, wtvr location
• opposite: same magnitude, opposite direction

Question 9

what is true if |AB|=|BA| but they point in diff directions?

Answer 9

|AB|≠|BA|
|AB|= -|BA| and -|AB|=|BA|

Question 10

resultant

Answer 10

when adding two or more vectors, the single vector is the addition of them

Question 11

what happens if you add two opposite vectors

Answer 11

• the resultant is the zero vector
• combined effect is the zero vector

Question 12

how to find resultant when adding vectors

Answer 12

• parallelogram
• triangle (tip to tail)

Question 13

how to find resultant when subtracting vectors (a-b)

Answer 13

• adding the opposite: do a+(-b) and flip the b arrow
• tail to tail and find resultant

Question 14

3 properties of vector addition

Answer 14

• commutative property
• associative property
• identity property

Question 15

commutative property

Answer 15

u+v = v+u

Question 16

associative property

Answer 16

w+(u+v) = u+(v+w)

Question 17

identity property

Answer 17

v+0 = 0+v

Question 18

overall magnitude when adding two vectors acting in same direction

Answer 18

sum of two individual magnitudes

Question 19

overall magnitude when adding two vectors acting in opposite direction

Answer 19

difference of two individual magnitudes

Question 20

pythagorean theorem + when to use

Answer 20

c² = a² + b²
- know 2 sides, want 3rd side

Question 21

SOH CAH TOA + when to use

Answer 21

• know two sides, want angle
• know 1 side and 1 angle, want side

Question 22

sine law + when to use

Answer 22

a/sinA=b/sinB=c/sinC
- know 2 sides and opposite angles, want angle
- know 1 side and all angles, want side

Question 23

cosine law (w/o fraction)

Answer 23

a² = b² + c² - 2bc(cosA)
- know 2 sides and contained angle, want 3rd side

Question 24

cosine law (w/ fraction)

Answer 24

cosA = (b² + c² - a²) / 2bc
- know 3 sides, want angle

Question 25

what doe it mean when a question says "angle between the two vectors is ___"?

Answer 25

angle between vectors when placed tail to tail

Question 26

how many decimal places in answer for magnitude/angle?

Answer 26

- one place for magnitude - whole number angles

Question 27

what is it called when two vectors are parallel?

Answer 27

- colinear - can be translated onto same straight line

Question 28

scalar multiples of vectors are...

Answer 28

colinear

Question 29

4 rules of scalar multiplication

Answer 29

1. if k is greater than 0, then ka is same direction and magnitude is ka 2. if k is less than 0, then ka is opposite direction and magnitude is ka 3. if k=0, the result is zero vector 4. distributive property is k(u+v) = ku+kv

Question 30

how to find unit vector

Answer 30

1. draw diagram, make parallelogram, pick a triangle 2. make table 3. find magnitude 4. equate side (x) to [u+v] to 1, then set side (x) to reciprocal of side's exact value...all goes to 1 5. draw both lines and label

Question 31

how to set up airplane velocity Qs

Answer 31

- airplane velocity: airspeed - wind velocity: velocity relative to ground - resultant is ground velocity

Question 32

airplane Q triangle set up

Answer 32

- hypotenuse: air velocity - vertical line: wind velocity - bottom line: ground velocity

Question 33

steps to solving airplane velocity Qs

Answer 33

1. draw vectors on cartesian planes and combine them 2. make table 3. find magnitude 4. make another compass based on where the needed vector comes out of the origin. find the inside angle using a formula and then use the z-pattern to determine the angle in relation to south/north

Question 34

how to find equilibriant force?

Answer 34

1. find resultant 2. make compass w/ just the resultant vector, extend it opposite 3. determine new angle/direction, keep magnitude the same

Question 35

how to solve tension in the rope in a mass hung by two ropes?

Answer 35

1. diagram: fg=mg, ropes make angle with CEILING, use z-pattern 2. triangle: stack z-pattern on top of each other, use z-pattern again to find angles inside triangle. fg=mg will point upwards 3. make a table 4. find the magnitude (should have a pair)

Question 36

how to solve forces in the rope in a mass hung by one rope pulled back?

Answer 36

1. draw diagram, determine fg=mg 2. make triangle with side lengths. solve for angle 3. use the angle for another triangle w/ forces 4. solve for forces using SOHCAHTOA

Question 37

how to resolution problems?

Answer 37

1.make a diagram 2. label horizontal/vertical as fx and fy 3. solve for absolute value of fx and fy using SOHCAHTOA (u will have angle + hypotenuse)

Question 38

what do the angles in a parallelogram add up to?

Answer 38

360 degrees