A tug, exerting a pulling force of 800 N due north, tows a barge through a distance of 1 km in a direction `30^(@)E` of north. What is the work done by the tug?

Explanation

To solve the problem of calculating the work done by the tug, we can follow these steps:

### Step 1: Understand the Given Information
We have a tug exerting a pulling force of \( F = 800 \, \text{N} \) due north. The barge is towed through a distance of \( d = 1 \, \text{km} = 1000 \, \text{m} \) in a direction \( 30^\circ \) east of north.

### Step 2: Determine the Displacement Vector
The displacement vector \( \mathbf{r} \) can be broken down into its components. Since the angle is \( 30^\circ \) east of north, we can use trigonometric functions to find the components:
- The northward (y-direction) component is given by:
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