Question

RIchidra Badstown Elizabethton wensboro Harisburg Danvill Pkeville Hazard Leitchfield LLLINOIS Campbellsville KEHT UCKY Madisonville Black Mounta 4145 Paduca Bowing Green Somenet London Princeton Glasgow Hopkinsville Russellville Moicello iamaburg VIRGINLA Kingsportg erh JohineopCty Morristown egreenele Mayfield Murray Fankdin Springtield La Follette elerksyille Callatin Hendersoayille Paris ENNESSE Nashville Cookaville Knoxville Waverhy Seviergille nt Huntingdon 24Murfreesboro Creaniits Franklin Columbia Maryvile Asheville Lexington Cinatans Payton Shelbwille Lewisburg Pulaski Athens Hohenwald HORTH CAROLINA utal Henderson Savannah Lawrenceburg Winchester Cleveland Selmer Fayetteville Greenville Waltalla SOUTH Chattano Dalton LaFayette Calhoun oodall Moundain Florence Athens Brate4t Bald Huntsville Toccoa CAROLA Dablonega Gainesvilie Decatur ALABAMA Guntersville Scottsboip MISS. Russellville Fulton Ariderson" Forty Payne 1 Cartersville Canton G EORG A Rome Abbeville 1999 Microsoft Corp. All fightsareserved Calculations: To calculate the x-component of the resultant vector, Rcalc, simply add the x-components of each vector, A - D. Add the y-components of each vector to find the y-component of Rlc To calculate the magnitude of the resultant displacement, R, use the Pythagorus Theorem: 2 R,2112 R=[R To calculate the angle of the resultant vector using the components, use tan" (Ry/Rx) Objectives:To use a ruler and protractor to determine displacement vectors between locations on a map, and to learn practical applications for vector addition using both graphical and component methods. For this lab, we want to use the displacement vectors for several legs of a trip from Huntsville, AL to Knoxville, TN to find the resultant vector for the entire trip and compare this to the displacement vector measured directly from Huntsville to Knoxville. Procedures: 55 mi), draw straight lines representing each of the 1. Using the map provided (Scale 1 in following vector displacements: A is the displacement from Huntsville to Fayetteville. b. B is the displacement from Fayetteville to Manchester (located under the "v" in Shelbyville). C is the displacement from Manchester to Nashville. D is the displacement from Nashville to Knoxville. C d. 2. Measure the magnitude (distance) of each vector and record it in the table below. 3. Measure the angle (relative to EAST) of each vector and record below. 4. Calculate the x and y components of each vector. 5. Calculate the components of the resultant vector, Reale: Rx and Ry Calculate the magnitude and direction of the resultant vector Reale 7. Draw and measure the magnitude and direction of the resultant vector directly from Huntsville to Knoxville (this is Rmeas), and calculate the components, Rx and Ry (last 6. row). Compare your two answers for Reale and Rmeas - Data Table y-component VECTOR Magnitude Angle X-component A C D Ry= Rx= Reale Rmeas estions: 1. What is the total distance traveled? (Use the individual vector magnitudes) How does this compare to the magnitude of Rmeas? 2. Describe what you believe to be the major source(s) of error between Reale and Rmea

Answer 1

Answe Given that Scale 11n S5 mi The displaumutem huntsvile to A 0.3.inthes \6 S vi Here Cast A 87° rom amporunt Ax- A CosBA 16.5 Cos 87° Now dCmfonent AsineA le.s sing1° 16.umi L6.477Mi

o -) Now, 0.2ieky nd om X-Componat O.45am 3-Compenust y rB sinD LO.S8mi So

Now, ouxs = 2amly Here So, CCosOc -ompnd C aacosi0 omparut C sing 20.Gnui (03u24-ao.6733) imcky 28.5mily

Anglu om East Op cmpered DCOSGD Dx X B5t0s (-s9 20.23 mily 38. DSingo t-s) 38. 5 Sin 3.25aly 3.35) 32. 8531- Rmeas inche wmly angh

X 4u cosuUo 33 166 Companet ty Sinuo 33. T06 meas 8 magnitude Angle Y-ot Cormpentat Veto A 87 0.863 11 .q59 20.673 0.342 D -s 38.5 -3.355 38. 3S3 Reau 8.33 39.233 Ry = 44.753 59.9 - 33.o6 44 28, a83

The total isiance dovcllo- Heae The tote Distone hevdlledi= AtBtC L 88 Total Dislance dremllud, Heve The mamitade ef onu Rmaa ..L = a Pma ts dob This dislanc Rmcas

merjon Sour ce Here Enos blas Reals, and Rmeot The majo Sourte aast lovnt (1 inh SS aceuoay in Each masuremert 4hurc is fn So1 RealR (31. 8.33)uu.7) Rcale 59.92 uu. 753 tan -' cake 39.833 u2.32