How to Troubleshoot Apps for the Modern Connected Worker
1 - vectors notes
1. Vector vs. Scalar
Vector Ex. Force
magnitude & direction Weight
(amount)
Velocity
Scalar Acceleration
magnitude Ex. Mass
Time
Money
Distance
2. Vector logistics
Vectors are represented by an arrow
Tells
direction
Length tells magnitude
Coordinate axis are used to represent position
North 10 N @ 45
+y 90°
180° +x
West -x East
0°
270° -y
South
Vectors are the same no matter where they are located, as long
as the magnitude and direction are the same!
3. Resultant
a single vector that replaces two or more vectors
1. Adding vectors A = 5.00 N @ 0.00°
5 B = 7.00 N @ 0.00°
7 R = 12.0 N @ 0.00°
2. Subtracting vectors A = 5.00 N @ 0.00°
(special case of addition) B = 7.00 N @ 180°
5
7
A + B = 5 + -7 = -2 or R = 2.00 N @ 180°
4.
5. 3. Adding at 90 A = 7.00 N @ 0.00°
B = 5.00 N @ 90.0°
Remember:
Resultant is from
beginning to end! 5
7
How do you draw this?
Parallelogram.
Draw dotted lines parallel to 5
original vectors.
Draw resultant from solid 7
lines to dotted lines.
6. How do you calculate the resultant?
Magnitude
Pythagorean theorem
5
Direction
SOHCAHTOA
2 2 opp 7
R 5 7 8.60N tan
adj
theta
Is the angle in first
5
reference to the tan 1
inside
origin? If not, add 7 angle you
back to 0. 35.5 come to
from 0
7. yt. M = 54.0 N @ 10.0°
O = 35.0 N @ 100° R
35
2 2 54
R 54 35 64.4N Steps:
opp
tan 1.
adj
35 2. draw a picture
1
tan
54 3. pythagorean theorem
32.9 +10 = 42.9° 4. inverse tangent
5. add angle back to zero
8. Components
Components 2 vectors that replace 1 vector
1 is always on the x – axis M My
1 is always on the y – axis
A Mx
Ay yt Px
Cx
Py P
Ax C Cy
Components are always at right angles.
Components are independent of each other!
9. A = 87.0 m/s @ 40.0
How do you mathematically find Ay & Ax?
opp
SOHCAHTOA cos
adj sin
adj
hyp
Set angle theta. cos 40
Ax sin(40)
Ay
87 87
Ax 87 cos 40 Ay 87 sin(40)
A
Ay When finding components, it
will always be this way!
Ax = mag cos (angle)
Ax
Ay = mag sin (angle)
y sin, because x is cos
10.
11. Vectors: 90°
To add vectors that are not at 90° to each
other, the vectors must first be broken
into their components.
ex. A = 10.4 m/s @ 75°
B = 6.7 m/s @ 25° R
Ay
A
B
By
Ax
Bx
12. Steps:
1. components find xtot & ytot
2. draw a picture
3. pythagorean theorem
4. inverse tangent
5. add angle back to zero
13. ex. A = 10.4 m/s @ 75°
B = 6.7 m/s @ 25°
Ax = 10.4 cos 75 = 2.69 Ay = 10.4 sin 75 = 10.0
Bx = 6.7 cos 25 = 6.07 By = 6.7 sin 25 = 2.83
xtot = 8.76 ytot = 12.83
ytot = 12.83
R= (8.762 + 12.832)
R R = 15.5
θ = tan-1 (12.83/8.76)
θ = 55.9°
θ
R = 15.5 m/s at 55.9°
Xtot = 8.76