To calculate the work done by Carlos in pulling the car, we must use the formula for work which incorporates the force applied, the distance moved, and the angle between the direction of the force and the direction of motion. The formula for work is:
[tex]\[ \text{Work} = F \cdot d \cdot \cos(\theta) \][/tex]
Where:
- [tex]\( F \)[/tex] is the force applied (2000 N),
- [tex]\( d \)[/tex] is the distance moved (30 m),
- [tex]\( \theta \)[/tex] is the angle between the force and the direction of motion (15°).
First, convert the angle from degrees to radians because cosine functions in most calculators and programming languages use radians. The conversion from degrees to radians is achieved by:
[tex]\[ \theta_{rad} = \theta_{deg} \cdot \left( \frac{\pi}{180} \right) \][/tex]
So,
[tex]\[ \theta_{rad} = 15° \cdot \left( \frac{\pi}{180} \right) \][/tex]
Now, we can plug the values into the work formula. Remember that [tex]\(\cos(15°)\)[/tex] should be calculated after converting 15° to radians.
[tex]\[ \text{Work} = 2000 \, \text{N} \cdot 30 \, \text{m} \cdot \cos(15°) \][/tex]
Evaluating the cosine term:
[tex]\[ \cos(15°) \approx 0.9659 \][/tex]
Then:
[tex]\[ \text{Work} = 2000 \, \text{N} \cdot 30 \, \text{m} \cdot 0.9659 \][/tex]
[tex]\[ \text{Work} \approx 57955.55 \, \text{J} \][/tex]
After rounding to two significant figures:
[tex]\[ \text{Work} \approx 5.8 \times 10^4 \, \text{J} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{5.8 \times 10^4 \, \text{J}} \][/tex]
