524.sagews

Sage Tool 1

This worksheet is configured for use with Exercise 6 in Section 5.1.

Enter and plot the altitude data:

altitude=[1295.5, 1297.0, 1296.0, 1295.0, 1292.1, 1290.2, 1283.5, 1278.2, 1274.4, 1261.9, 1253.2, 1242.6, 1234.0, 1216.7, 1199.9, 1184.0, 1169.1, 1151.8, 1137.4, 1124.9, 1114.8, 1104.2, 1095.1, 1086.9, 1078.3, 1071.0, 1059.5, 1049.9, 1044.1, 1038.8, 1033.1, 1027.8, 1022.0, 1017.7, 1012.9, 1007.1, 1001.4, 995.6, 989.3, 983.1, 977.8, 971.5, 965.3, 959.1, 954.2, 947.5, 940.8, 933.1, 925.9, 920.1, 913.9, 908.1, 902.3, 895.6, 889.8, 884.1, 878.8, 874.0, 869.2, 864.8, 861.0, 855.7, 850.9, 846.1, 842.3, 838.4, 834.6, 829.8, 824.9, 820.6, 817.3, 813.9, 810.0, 805.7, 801.4, 797.1, 792.7, 787.9, 782.7, 777.8, 773.5, 768.7, 763.9, 757.7, 752.8, 748.0, 742.3, 732.2, 725.5, 718.2, 711.5, 705.7, 693.2, 681.2, 667.3, 656.2, 646.6, 638.9, 632.7, 626.9, 620.7, 614.4, 608.2, 602.9, 598.1, 593.8, 589.4, 585.1, 579.8, 575.5, 571.2, 566.4, 561.1, 556.3, 551.5, 546.2, 541.4, 534.6, 528.4, 521.7, 514.9, 508.2, 502.9, 498.1, 491.9, 485.6, 479.4, 474.1, 468.8, 464.5, 460.1, 455.3, 450.5, 445.7, 439.9, 435.1, 431.8, 427.9, 423.6, 418.8, 414.9, 410.6, 406.3, 400.5, 395.2, 389.5, 383.7, 378.9, 374.6, 370.2, 366.4, 362.1, 357.7, 353.9, 349.6, 345.3, 341.4, 337.6, 333.7, 330.4, 326.5, 321.7, 317.9, 314.5, 310.2, 305.4, 300.5, 296.2, 292.4, 288.5, 284.2, 280.4, 276.0, 271.7, 268.3, 264.0, 259.7, 256.8, 253.0, 249.6, 245.3, 240.5, 235.2, 230.9, 225.6, 220.3, 215.0, 210.7, 206.3, 202.5, 198.6, 195.3, 191.4, 186.6, 181.8, 177.5, 172.7, 168.4, 164.0, 160.2, 155.9, 152.0, 147.7, 141.9, 137.6, 129.9, 125.1, 122.7, 117.9, 111.7, 109.2, 106.8, 104.0, 100.6, 97.7, 94.8, 91.9, 89.1, 86.7, 85.2, 82.8, 81.4, 80.4, 85.7, 86.7, 87.6, 88.6, 90.0, 88.1, 86.7, 85.2, 84.3, 83.3, 82.3, 81.8, 81.4, 81.4, 81.4, 81.4]

plot1=point([(i+1,altitude[i]) for i in range(len(altitude))],pointsize=2)
show(plot1,axes_labels=['Time (sec)','Altitude (meters)'])

m=1
b=200
var('t')
plot2=plot(m*t+b,t,0,240,color='red')
plot1+plot2

m*3600/1609;numerical_approx(m*3600/1609)

3600/1609 2.23741454319453

Convert meters per second to miles per hour:

Choose values for slope $m$ and $y$-intercept $b$ to make the line fit the constant-velocity part of the data.  (The given values are not correct.)