Question

Summary of Christopher Columbus’ first voyage in 1492. The voyage is simplified into the following displacement segments. Round to whole number as you work through the problems.
1) Palos de la Frontera (Spain) to Canary Islands: 1400 km; Southwest (50 deg south of west)
2) Canary Islands to San Salvadore (Bahamas): 7600 km; West
3) San Salvadore (Bahamas) to Cuba: 900 km; Southwest (45 deg south of west)
4) Cuba to Hispaniola & La Navidad: (Current Haiti/Dominican Republic island) 700 Km; Southeast (30 deg below east)
5) Hispaniola/La Navidad to Palos de la Frontera (Portugal): 6530 km; Northeast (40 deg north of east)

What is the overall (net) displacement of all 5 segments in East-West direction?

What is the overall (net) displacement of all 5 segments in North-South direction?

What is the magnitude of the resultant displacement of the entire voyage?

What is the direction of the resultant displacement of the entire voyage?

Answer 1

1] Eatern Displacement = -1400* cos 50 degree -7600-900*cos 45 degree+700*cos 30degree+6530*cos 40 degree

= -3527.8 km

hence East west displacement = 3527.8 km west

2] Northern displacement = -1400* sin 50 degree -900*sin 45 degree-700*sin 30degree+6530*sin 40 degree

= 2138.5 km north

3] Magnitude = sqrt(3527.8^2+2138.5^2)

= 4125 km

4] direction = arctan(2138.5/-3527.8) = 31.2 degree north of west