1. break each vector into its components1.
45°
17.0
15°
30°
24.0
28.0
X =
Y =
X =
Y = - 7.2
X =
Y =
10°
52.0 19
X = 0.0
Y = + 19
X = + 9.0
Y =

2. 80.7 m @ 63.5° south of east X Y + 12.0 - 20.8 + 27.0 - 7.2 - 12.0
add all the X and Y components separately X Y
+ 12.0
- 20.8
+ 27.0
- 7.2
- 12.0
- 12
0.0
+ 19
+ 9.0
- 51.2
° south of east
36 m
72.2 m
+ 36.0
- 72.2
Total distance = = 140 m

3. How to determine Intervals
Decide on an appropriate scale for each axis.
Choose a scale that lets you make the graph as large as possible for your paper and data
How to determine Intervals
Population
(millions)
Time
(years) 5 8 20 16 45 24 80 32
The interval is decided by your scale.
In this case your y-scale would be from 0 – 80 and your x-scale would be from 0 – 32 .
The graph paper is 8 x 7

4. Choose an interval that lets you make the graph as large as possible for your paper and data10
80 ÷ 8 = 10
32 ÷ 7 = 4.57
Always
round
up! 5

5. Population (millions)
Population versus time 80
population is proportional to time squared 60 40
p ∝ t2
Population (millions) 20 10 20 30
Time (years)

6. Linearize 1024 ÷ 7 = 146 The interval is decided by your scale.
Population
(millions)
Time2
(years2) 5 64 20
256 45
576 80
1024
The interval is decided by your scale.
In this case your x-scale would be from 0 – and your y-scale would not change.
The graph paper is 8 x 7
1024 ÷ 7 = 146
150

7. slope 0.078 million/years2 Must use points that fall on the line
population versus time squared 80
Must use points that fall on the line 60
poopulation (millions) 40
0.078 million/years2 20
300
600
900
Time squared (years2)

8. How many minutes are in 2.5 hours?
Conversion factor
2.5 hr x min = min
1 hr
cancel
By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

9. How many seconds are in 1.4 days?
1.4 days x 24 hr x ??
1 day
60 min
1 hr
60 sec
1 min x
= 120,960 seconds

10. 0.3375 mph 0.0288 m3/hr 15 cm 1 m 1 mile 60 sec 60 min x x x = x sec