A car goes 5.0 km south, 2.0 km West and 1.0 km North. Find the resultant vector using both: POLYGON METHOD ANALYTICAL METHOD

Question

the resultant vector and the angle is the unknown

 

Answer 1

To use the polygonal method, label the point where the car begins its journey as (0,0), with positive x denoting East and positive y denoting North. The car's movement of 5.0 km South has the representation (0,-5) and 2.0 km West the representation (-2,0). Drawing vectors of lengths 5 units and 2 units with the correct directions (in the -x direction and -y direction, respectively) and placing them tip-to-tail gives a resultant vector of (-5,-2). Add this resultant vector to the vector (0,1) (which represents a trip of 1.0 miles North) in the same way will give you the correct answer of (-5,-1), or 5 km West and 1 km South.

 

To do this analytically, just compute the vector sum (-5,0) + (0,-2) + (0,1) = (-5,-1).

Answer 2

North is positive y (up) and east is positive x (right).

 

Analytical method:

• Starting Vector = [0  0]
• 5 km south = [0  0-5] = [0  -5]
• 2 km west = [0-2  -5] = [-2  -5]
• 1 km north = [-2  -5+1] = [-2 -4]

 

For the polygon method:

• Draw an xy coordinate plane
• first vector starts at origin, goes straight down 5 units (arrow end)
• second vector starts at arrow end of first vector goes left 2 units (arrow end)
• third vector starts at arrow end of second vector and goes straight up one unit.
• Resultant vector starts at origin, ends at arrow end of third vector