Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.80×106 N , one at an angle 14.0 ∘ west of north, and the other at an angle 14.0 ∘ east of north, as they pull the tanker a distance 0.800 km toward the north. Part A What is the total work done by the two tugboats on the supertanker?

W = 1,049 10⁹ J

Explanation:

Work is defined by the relation

         W = F. d = F d cos θ

where tea is the angle between the forces and the displacement.

The total work is the sum of the work of each tug.

Tug 1

       W₁ = F d cos θ₁

the angle measured from the positive side of the x-axis is

       θ₁ = 14 + 90 = 104º

tugboat 2

             W₂ = F d cos θ₂

             θ₂ = 14

we substitute

             W = F d cos θ₁ + F d cos θ₂

             W = F d (cos θ₁ + cos θ₂)

let's calculate

             W = 1.80 10⁶  800 (cos 104 + cos 14)

             W = 1,049 10⁹ J

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