On November 1^st, 1519, Ferninand Magellan and crew reached the equator in the m

Question

On November 1^st, 1519, Ferninand Magellan and crew reached the equator in the mid Atlantic (longitude 30 degrees West). They continued sailing around the Cape of Good Hope, and crossed the Pacific, reaching the equator again in the area of the Mariana Islands on March 6^th, 1521 (longitude 140 degrees East). The total distance traveled between these two points, including stops along the way, was 22, 000 miles. (a) What their average speed (in mph) between these two dates? (b) What is the displacement vector d vector (in the xy plane) pointing from their initial location to their final location? Take the xy plane to pass through the equator, with origin at the center of the earth, and take the y axis so that it passes through the origin, from longitude 0 degrees to 180 degrees, and the x axis so that it passes through the origin, from longitude 90 degrees west to 90 degrees east. (c) What is the time-average velocity vector V vector bar for the time between 11/1/1519 and 3/6/1521? What is its magnitude |v vector bar|?

Explanation / Answer

given

distance travelled, d = 22,000 miles

a. time taken for distance d = march 6 1521 - november 1 1519 = 491 days

Vav = 22,000/491*24 = 1.8669 mph

b. initial coordinates wrt to the coordinate axes as explained

(xi,yi,zi) = (-Rsin(30), -Rcos(30)) where R is radius of earth

final coordinates (xf,yf,zf) = (Rcos(50),Rsin(50),0)

so displacement vector d = ((xf - xi)i + (yf - yi)j) = R(1.142, 1.632,0)

R = 3959 miles

so d = 4521.178i + 6461.088j

c. velocity vector = d/491*24

V = (4521.178i + 6461.088j)/491*24 = 0.383I + 0.548 J MIL / HR

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