The magnitude and direction exerted by two tugboats towing a ship are 1640 kilograms, N35°W, and 1270 kilograms, S60°W, respectively. Find the magnitude, in kilograms,

Question

and the direction angle, in degrees, of the resultant force

Answer 1

The easiest way to solve this problem is to break up the two vectors into x- and y-components and then add the separate components.

1) Break up the two vectors into components:

The first vector (N35W) is in quadrant 2, and forms an angle of 125 degrees (= 35 + 90) with the x-axis. Thus,

x₁ = 1640 cos (125)

y₁ = 1640 sin (125)

The second vector is in quadrant 3, and forms an angle of 210 degrees (= 270 - 60) with the x-axis. Thus,

x₂ = 1270 cos (210)

y₂ = 1270 sin (210)

2) Add the individual x and y components to get the components of the resulting vector:

x_total = x₁ + x₂

y_total = y₁ + y₂

3) Use the total x and y components to find the magnitude and direction of the resulting vector:

magnitude = √(x_total² + y_total²)

direction = tan^-1(y_total /x_total )