To calculate the work done by the dog on you, we use the formula:

$W = F \cdot d \cdot \cos(\theta)$

Where:

• $F$ is the force applied ($50 \, \text{N}$),
• $d$ is the displacement ($10 \, \text{m}$),
• $\theta$ is the angle between the force and the displacement ($20^\circ$),
• $\cos(\theta)$ accounts for the horizontal component of the force.

Substituting the values:

$W = 50 \cdot 10 \cdot \cos(20^\circ)$

Calculating:

• First, find $\cos(20^\circ)$. Using a calculator: $\cos(20^\circ) \approx 0.9397$

• Now, compute: $W = 50 \cdot 10 \cdot 0.9397 = 469.85 \, \text{J} \, (\text{Joules})$

Final Answer:

The work done by the dog is approximately 470 Joules.

Would you like further clarification or related details? Here are some additional questions to explore this concept:

1. What is the role of the angle in the work formula?
2. How would the work done change if the angle increased to $45^\circ$?
3. What happens to the work if the displacement or force doubles?
4. Can work be negative in similar scenarios? If so, when?
5. How does this relate to energy conservation?

Tip: Always resolve the force into its components when it is applied at an angle to the displacement.