To calculate the work done on the sled by the child, we can use the formula for work, which is given by:
\[ W = F \cdot d \cdot \cos(\theta) \]
Where:
- \( W \) is the work done,
- \( F \) is the force applied,
- \( d \) is the distance moved in the direction of the force,
- \( \theta \) is the angle between the force and the direction of motion.
In this case:
- \( F = 75 , \text{N} \)
- \( d = 40 , \text{m} \)
- \( \theta = 20^\circ \)
First, we need to find \( \cos(20^\circ) \):
\[ \cos(20^\circ) \approx 0.9397 \]
Now we can substitute these values into the work formula:
\[ W = 75 , \text{N} \cdot 40 , \text{m} \cdot \cos(20^\circ) \]
Calculating this:
\[ W = 75 \cdot 40 \cdot 0.9397 \] \[ W = 3000 \cdot 0.9397 \] \[ W \approx 2819.1 , \text{J} \]
Therefore, the work done by the child on the sled is approximately 2819.1 Joules.