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 find the work done by the tug, we can follow these steps:

### Step 1: Identify the force and the distance
The tug exerts a pulling force of \( F = 800 \, \text{N} \) in the north direction. The barge is towed through a distance of \( d = 1 \, \text{km} = 1000 \, \text{m} \) at an angle of \( 30^\circ \) east of north.

### Step 2: Break down the distance vector into components
We need to resolve the distance vector into its components. The distance vector \( \mathbf{r} \) can be expressed as:
\[
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