break each vector into its components 1. 45° 17.0 15° 30° 24.0 28.0 X = - 12.0 Y = - 12.0 X = + 27.0 Y = - 7.2 X = + 12.0 Y = - 20.8 10° 52.0 19 X = 0.0 Y = + 19 X = + 9.0 Y = - 51.2

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 80.7 m @ 63.5° south of east 36 m 72.2 m + 36.0 - 72.2 Total distance = 24.0 + 28.0 +17.0 +19.0 +52.0 = 140 m

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

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

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 – 1024 and your y-scale would not change. The graph paper is 8 x 7 1024 ÷ 7 = 146 150

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)

How many minutes are in 2.5 hours? Conversion factor 2.5 hr x 60 min = 150 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!

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

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